From the US Naval Historical Center's photo archives ---
USS Black (DD-666)
At sea, following her mid-1950s modernization, in which she lost one 5"/38 gun mount and received three 3"/50 twin mounts.
Mount 53 (that is the one just forward of the raised gun platform goes away. Add a raised director structure in its place. The 3"/50s replace the twin and/or quad 40s in the raised raised tub aft and in the waist tubs.
Note too the square bridge and low MK37 director. The Tam kit is the early round-bridge version with the high MK37. You would be better served in starting with the Trimpeters 'The Sullivans' (It is a square-bridge/low Mk37 and has the large gun tubs you will need as well as the midship director tower).
The MK37 is the later version with the dish instead of the butterfly-shaped radar antenna.
Veterans Models used to make some aftermarket 3"/50s. But they were overpriced (IMO) and you needed to buy them along with other details you may or may not use. They had been imported by Commanders/Iron Shipwright -- but they have been removed from their website so I guess they are no longer available. The Tom's Modelworks square-bridge conversion for the Tam Fletcher (now OOP) had some 3"/50s in it. If you come up blank, I may have some in the spares box from another project.
Note too the hedgehog boxes under the bridge wing, along with reload lockers between the bridge and Mount 52.
Big changes in the mast too. The kit mast (Tam or Trump) is a single pole mast. The Black, like most post-war Fletcher refits got a tripod mast to support the larger radar array.
I would try to locate a copy of the Anatomy of the Ship - The Sullivans. It has good pictures and line drawings which include this sort of weapons/sensor layout.