On the TypeScript team, we just use regular code coverage tools on the compiled JavaScript. We’ve found this to be more than sufficient, since usually for code coverage you are looking at total coverage % (which doesn’t change significantly) or are deep-diving at expression-level (which also doesn’t change significantly).
If you found a tool that supported it (I’m not aware of any yet), you could in theory use the source maps emitted by the compiler to map the coverage data back to the TypeScript code. It’s probably not worth the trouble.