If I recall correctly, AM2 boards will support AM2 cpus and AM2+ cpus. Not AM3 cpus.
You will probably do best with an Athlon 64 or some Phenom processors (9000-series, 920, 940)
The definition of AM2 and AM2+ is so vague it's probably just weasel talk from the lawyers/marketers more than a concern for end users.
I have a ASUS M2A-VM that I bought as soon as they were available. The web documentation at time of release, the product box that I'm using to increase the height of my monitor stand, the manuals all said it was AM2. A few months after AM2+ was out the web documentation changed to calling it AM2+. Eventually they released a BIOS that allows this board to us an AM3 processor.
I'm literally typing this message on a PC with a X3-720 BE in a 690G "AM2" motherboard.
I'm sure there is a board somewhere without the BIOS support for the chip you might want to put in it. I'm sure there is a board somewhere that was made so cheaply that it isn't in spec electrically to support AM2+/AM3 cpus in a "AM2" socket. I don't know that I'd consider those the norm though.
If it's cheap buy the CPU and see what happens. If it isn't research it by going to the web site for the motherboard manufacturer and reading the BIOS change logs / release notes and/or looking for a supported CPU list.
Even if the BIOS doesn't specifically support a CPU if it supports the general family of CPUs it may work but display the wrong name during POST. Or put another way the possibilities are
1. Won't boot at all with the chip in place
2. Will boot but doesn't identify the CPU properly
2a Is unreliable with that CPU
2b Is reliable with that CPU
3. Boots and identifies CPU properly
3a Is unreliable with that CPU
3b Is usable with that CPU but not as reliable as with the old CPU
3c Is more reliable with the new CPU than it was with the old CPU
In the case of the X3-720 BE on my 690G board from ASUS I got 3c. My memory runs in ganged mode (faster in a couple of ways), L3 cache makes everything seem smoother/faster, higher speed DDR2 is supported thanks to the memory controller being in the CPU not on the motherboard, and so on...
But if you aren't willing to waste money trying it yourself you might want to contact ECS tech support before getting anything.