Hey Andrew, That's a good point. I had assumed he was looking for a GAR-1 or GAR-2, as these were the original Falcons, and are very similar...IIRC, the -2 was only an inch or two longer, the main difference being the seeker heads. If he is looking for a later AIM-4, such as a Super Falcon, introduced in...gimme a sec, 1958, then we can look at quite a bit more kits.
The thing that will probably help the most is that the Falcons and Super Falcons were not called AIM-4 anythings until later on, 1962, I believe. So, if the kit includes an AIM-4 something, rather than a GAR- something, that gives us an idea as to the date. Here's the breakdown of the variants as well as some pictures.
1. AAM-A-2, renamed to the F-98, renamed again to the GAR-1 (AIM-4)
2. GAR-1D (AIM-4A)
3. GAR-2 (AIM-4B)
4. GAR-2A (AIM-4C)
5. GAR-2B (AIM-4D)
6. GAR-3 (AIM-4E)
7. GAR-3A (AIM-4F) Radar seeker in picture below
8. GAR-4A (AIM-4G) IR seeker in picture below
9. XAIM-4H
10. GAR-9 (AIM-47)
11. GAR-11 (AIM-26)
12. AGM-76! The picture below is of the XAGM-76.
These were all referred to as the 'Falcon', so there is quite a bit of confusion. If any of these look like what should be in the set, then we'll know what missile you are looking for.