I think your best bet would be an in-home daycare. Every child care provider (in-home and center based) have requirements as far as the maximum number of children they have. A center would be more likely to be impacted with fluctuating participation vs a home based provider.
Check out Virginia Licensed Daycare Providers and FFX County Licensed Daycare providers, links below. The county licensed ones would all be home-based. Just because someone is licensed with the county doesn't mean they are licensed with the state.
http://www.dss.virginia.gov/facility/search/cc.cgi
http://www.fairfaxcounty.gov/childcare/search/