Certified GKH Gardening Expert
This article should help: https://www.gardeningknowhow.com/edible/vegetables/tomato/tomato-blossom-rot.htm
Use the tips from the article but apply them to containers instead. Make sure you have adequate drainage and fertile, well-draining soil. Fertilize with low nitrogen/high calcium fertilizer. Give them plenty of water. Add mulch to the top of your containers (straw works well) to help retain moisture and insulate the soil.