Selling on Ebay or doing Fea marketing/Yard Sales would be a way to make some money without jeopardizing your unemployment.
Odd jobs like handyman work is also another good way to make some quick cash. The key is to do things where earnings are unreported. In today's economy it is very hard to get people to let go of their money. Even finding a part time job is very difficult.
If you can do computer repair, placing ads strategically around your area may bring some repair jobs that will not reflect on the unemployment and should pay well.