Children's to-go drink cups

We offer free refills 20 oz fountain drinks in foam cups (no logo). We would like to have plastic stadium-type children’s cups with our logo. Anyone have any good input? Suppliers, costs, ideas?

We bought stock Italian themed cups from a company called Sherman Specialty. They were 11 cents each, including the lid. Their website is http://www.shermanspecialty.com/

I was unable to find anybody to do a custom print for less than a 20,000 run.