How small is "small"? When I hear "betta" I usually imagine a 3 to eight gallon tank. If you're a new hobbiest in the saltwater department, it's said that you should use a larger tank. In saltwater, there are a lot more chemical components that need to be taken note of and monitored than in fresh (ie. Ammonia, nitrites, nitrates, PH, Sg, Salinity, and many more). If you have a small tank, and theres a problem, that can get out of control extremly quickly. Think of it as a little kid peeing in the bathtub. It's disgusting because it's in such a small place, but there are countless people who pee in the large bodied lakes and oceans, and the water's fine.
As YummySalt stated above, copper is extreemly bad for corals. Most fish disease treatments have copper in them, and having even a small trace of that in your tank (especially if its a small tank!) will kill any coral. Read up on some of the sticked threads in the new hobbiest boards, they'll help a lot.