The CPUs supported by that motherboard would be listed on the eMachine website for that model, if at all. OEM's don't like you messing around with their equipment.
Your motherboard might be similar as HP and Compaq Desktop PCs - Motherboard Specifications, MCP61PM-HM (Nettle) | HP® Customer Support , which is also a NVidia GeForce 6100 based AM2 motherboard with processor TDP support of maximum 89W. You can find the detail information on your processor, from http://www.cpu-world.com/CPUs/K8/AMD-Athlon%2064%20X2%206000%2B%20-%20ADV6000IAA5DO%20(ADV6000DOBOX).html . It is an AM2 processor with TDP of 89W just accepted by that motherboard.
In fact, all the AM2+ and AM3 processors provide back-ward compatibilities, that is like what's in your current system based on Athlon II X2 235 (AM3). But for the stability, I suggest you to choose your mentioned processor, Athlon 64 X2 6000+. That is the best for your system!