The best way to store blackberries for use at a later date is to rinse them and then put them on a cookie sheet in your freezer until they are frozen solid. Then transfer them to a Tupperware type container and keep in the freezer until you want to use them.
I have found that if I store blackberries or raspberries in a airtight container, they last much longer than the ones stored in the paper pint container from the farmer's market.