IC for 4 Kbytes of RAM
Tricky. Most of them would be about 25 years old by now, and capacities mostly went straight from 2 kbytes (e.g HM6116) to 8 kbytes (HM6164) 

I'd go for 8 kbytes... Similar parts are just still available e.g. Cypress CY6264 If 8k is not permitted, wire the highest address bit to '0' and keep quiet about it...