I think it depends a lot on where you are. If you are someplace where there are a lot of cleared employers (Wash DC area, Los Angeles, Denver, Huntsville etc) then you may be able to find some kind of part-time gig requiring a clearance. If you are near a major government facility you may be able to get a job with a cleaning services company.
Many employers dont want to deal with part-time employees; it seems that once they find someone who is cleared, they want to put them to work full time on the contract and maximize the amount that can be charged to the contract.