I've never grown strwberries in containers. This link may have some helpful info on some varieties that may do okay for you. Let us know how it work out.
http://www.ces.ncsu.edu/depts/hort/hil/hil-8205.html

Chandler is the best strawberry for the Carolinas.

Sweet Charlie and Allstar grow well for us in open ground. Both set "daughters" so where do you plan on having them next year (BTW - the third year (granddaughters) have the biggest, sweetest berries).

Nancy the nancedar