BNC cable to composite video cable conversion
By a "composite video connection" I assume you mean an RCA connector such as you see on the back of a TV. In that case you need a simple "BNC female to RCA male" adapter, which looks like  

You can find these at places like Radio Shack, or at lots of places on the net.

ETA: In comment, a preference for direct connections due to reliability issues was expressed. The answer to that is simple - yes, such connectors are readily found. RCA connectors are widely used for home video/RF inputs, and something like  are readily available. Search on "RCA connector RG59" as a starting point.

END EDIT