A really old and slow Athlon X2 would be the best you can get for you system, 939 went out of production 4+ years ago. AMD has since had socket AM2 with DDR2 memory, than AM2+ with new K10 processors, and now socket AM3 with DDR3 memory and improved 45nm varients of K10 processors(some refer to it as k10.5).
In all honesty a new $60 cpu will walk all over anything made for socket 939, and in many cases you can get a new cpu/motherboard/ram for the cost of a decent used 939 cpu. It's time to upgrade more than just your cpu.
Yup, the FX-60 would be best, and right below that the 4800X2. Problem is, both are going for so much on eBay that you should buy a new budget AM3 CPU/board/and RAM for the same price . I would only consider upgrading your CPU if you had a nice high end board and dual GPU setup while simply wanting a little more CPU power to complement your card. Since your board is only meant for single cards, and mid range at best, I wouldn't bother.
+1 upgrade the whole system, unless you can find a supported cpu for a decent price. (Just know the lowest end dual core from amd on their new socket is $60, and will probably wipe the floor with the best you can get for that mobo)