AM2 boards work fine with AM2+/AM3 processors if the manufacturer has an updated BIOS to support the new architecture. I personally ran a Phenom II X4 AM3 processor on my old AM2 board for a while before upgrading. I've never heard of an AM2 board hurting an AM2+/AM3 processor.
The problem is, OEM's like emachines rarely issue BIOS updates for legacy products. You may be able to lookup the motherboard manufacturer (Foxconn, or similar) and find a BIOS update to allow an AM2+/AM3 upgrade.
I say you have two options:
#1: Go with an Athlon II X2 knowing that it may not work. If it doesn't work, you could always pop the old CPU back in and pay a restocking fee when you return the new CPU as a lesson learned.
#2: Get an AM2 Athlon 64 X2 on eBay which is guaranteed to work. There are plenty of 5600+, 5800+, etc. processors out there for sale. Any of them would be a nice upgrade from a single core Sempron. Don't pay too much for one though, since you are nearly due for an entirely new system. Also, you might want to stay away from the higher wattage chips... look for 65W chips and under.