Unfortunately this one has a pretty simple answer.
To my knowledge, the only one of the original six that's ever actually been the subject of a kit, in either plastic or wood, is the Constitution. Revell, Monogram, and Imai have, at various times, issued their Constitution kits in slightly modified form with the name "United States" on them, but those kits didn't actually represent the United States accurately. (The big, 1/96 Revell one did make a half-hearted attempt at reproducing the raised quarterdeck and "roundhouse" of the real ship, but that kit was on the market only briefly and is now something of a collector's item.)
At least one of the HECEPOB wood kit companies (HECEPOB = Hideously Expensive Continental European Plank On Bulkhead) has released a kit labeled Constellation, but it's based (more or less - with typical HECEPOB lack of concern for reality) on the 1850's corvette now preserved at Baltimore. Naval historians - including, nowadays, the people responsible for the preservation of the ship - are almost universally agreed that this vessel is not the 1797 frigate of that name.
The available documentation suggests that the President was extremely similar to the Constitution. Quite a few modelers have converted Constitution kits into models of the President. (The big differences between the two ships seem to have amounted to little more than the bow and stern decorations - and since there seems to be no detailed record of what those of the President looked like, you can just about get away with the "conversion" by changing the name on the transom of a Consitution kit.
To my knowledge, the only representation of the Chesapeake in kit form that's ever been released is the tiny (though excellent) cast metal wargamers' version by Skytrex. (I know that sounds like a bold assertion, and I certainly can't claim to know about every single sailing ship kit that's ever been manufactured. But I've certainly never heard of another Chesapeake kit. That the manufacturers would find her an unattractive subject is certainly understandable.) And I don't think anybody's ever issued a Congress kit.
Currently there are two plastic Constitution kits on the market, both from Revell-Monogram. The 1/192 one dates from 1956. At that time it represented the state of the art, and in many ways it holds up pretty well by modern standards. It's about 18" long, and, with one big exception, represents the ship pretty much as she appeared in 1956. (The exception is the figurehead. Revell includes a nice reproduction of the Andrew Jackson figurehead that the ship wore in the 1830s and 1840s.) Its big weakness, in terms of accuracy, is its representation of the big hatch in the middle of the spar deck. Instead of an opening looking down into the gundeck, with ladders in the corners, it's a solid piece of plastic. (The guns on the gundeck are nice little plastic castings sitting on little "shelves" cast integrally with the hull halves. In 1956 that was mind-boggling detail; the wood kits of that era had "dummy" gun barrels that plugged into holes drilled in the solid hulls.)
The other extant plastic Constitution is the big Revell-Monogram one, which dates from 1965. It's one of the best plastic sailing ship kits ever produced. It's also showing its age these days, but it certainly has the potential to be turned into a fine scale model. On the other hand, gjek says it's too big for his available display space - and I can certainly sympathize.
The late, lamented Japanese company Imai produced, very briefly, a Constitution on, if I remember right, about /150 scale. That one just might meet gjek's requirements. Imai kits were generally excellent. I don't think I've ever actually seen this one personally. (Imai was only on the scene briefly - at a time when my budget couldn't accommodate kits in that price range.) As I understand it, it represented the spar deck hatch the same way the little Revell kit does - i.e., with a smooth, solid surface rather than an open hatchway. To me personally, that's just not acceptable on that scale. But one could add a section of the gundeck under the hatch without too much difficulty, I guess.
That Imai kit was sold very briefly in the U.S. under the Monogram label. (I never even saw the box of one of those kits.) It also turned up (even more briefly) with a "U.S.S. United States" label, but didn't accurately represent that ship (i.e., no raised quarterdeck).
In 1969 Revell issued a Constitution in its short-lived "Simplified" series. This was an effort to bolster sales of sailing ship kits at a time when the plastic kit industry was having major problems. The kit was on about 1/159 scale and had an overall length of about 22 inches(according to Dr. Thomas Graham's excellent book, Remembering Revell Model Kits). It was a scaled-down version of the 1/96 Revell kit, with many of the details considerably simplified to keep the parts count down. ("Build a Legend In a Weekend!") Most of the ports on the gundeck were molded shut, though the kit contained a section of gundeck amidships, with vague representations of the 24-pounders molded integrally with it, and the hatch in the spar deck was a real hatch. For its intended market it wasn't a bad kit. But it's been off the market for a long time. (For the benefit of anybody who wants to look for it - Dr. Graham says it was issued under the kit numbers H-362 and H-357.)
At about that same time (the early or mid-seventies), Monogram produced a small series of highly simplified, if rather ingenious, sailing ship kits, including a Constitution. It was somewhat smaller than the 1/192 Revell kit, and featured such things as a one-piece hull and yards molded integrally with the masts. (Monogram was trying to keep the parts count really low. There was some discussion of this kit recently here in the Forum; it looks to me like an interesting artifact from a difficult period in the industry's history, but hard to take seriously as a scale model.) Aurora also produced a small Constitution. I don't recall having seen it outside the box, but on the basis of that company's other sailing ship kits I suspect it isn't worth looking for.
A few months ago Revell Germany announced that it was reissuing some older kits to celebrate the company's fiftieth (I think) annivesary. One of the kits on the list was a medium-sized Constitution. I don't know whether this is the "simplified" version or the old Imai one. I haven't heard anything of it recently; maybe a European Forum member knows more about it.
There are two excellent wood Constitution kits on the market: a plank-on-bulkhead one from Model Shipways depicting her as she appears today, and a solid-hull one from Bluejacket that reconstructs her War of 1812 configuration. Both of them are quite expensive, and a lot bigger than gjek's specifications. At least one of the HECEPOB companies makes a Constitution kit, but serious scale modelers avoid those...things...like the plague. I know of no other wood kits representing early American sailing frigates. (Model Shipways used to make two versions of the Essex on different scales, but they've been out of production for decades.)
This is a sad situation - a reflection of the state of this segment of the model kit industry. The unfortunate truth of the matter is that the range of plastic sailing ship kits never was very big. (Considered in terms of model airplane equivalents, it never got beyond the level of the Spitfire, Mustang, and B-52.) And nowadays it's just about dead. Revell used to be the world's leader in plastic sailing ship kits. The current Revell-Monogram catalog contains two sailing ships - both representing the same ship, one aged 51, the other aged 42.
Bottom line for gjeck: in plastic, your options are to (1) settle for the widely-available Revell-Monogram 1/192 Constitution (which, with some effort, actually could be turned into a nice model), (2) seek out an old Revell "simplified" version or an Imai one, or (3) buy a bigger house and tackle the Revell-Monogram 1/96 kit. If you want a President, you can do a fairly straightforward conversion from a Constitution kit. If you want the United States, you'll need to add a raised quarterdeck to a Constitution kit. If you want any of the other three (Constellation, Congress, or Chesapeake), your only option is scratchbuilding.
Well, for a "simple answer" that took up quite a bit of space. Sorry to be so depressing. It would be nice if the kit manufacturers would cater more effectively to sailing ship enthusiasts, but I see little reason for optimism that they're going to do so in the foreseeable future.