What is the type of the ROM chip
Any ROM/RAM according to JEDEC specification for that package can be used with a 3C509B
It's 28 pin connector, please see picture below.
Standard JEDEC DIL I'd say. The B model fits anything from 24 to 28 pin with capacities between 8 KiB (Type xx32) and 64 KiB (Type xx512). Sizes over 16 KiB do need a window setting. Pinout as seen here:

This includes
- PROM
- EPROM (usually named 27xx)
- EEPROM (often named 28xx)
- FLASH (often named 29Fxx or 28Fxx)
- Various MRAM
Which one to pick is up to your ability to program and reprogram. The B model does not only support EEPROM as ROM, but as well writing them, thus such might be the preferred solution.
In any case a peek at the 3C5x9B manual might be useful.
and where would you obtain it?
RC.SE is not suited for 'where to buy'-type questions. Pick the type you want to use and hit your preferred search engine with that part number. To find the right one you may try a parametric search at a major distributor first (and compare with its competitors :)).