My advice would be to compile your CoffeeScript to JS, then start from there. That's assuming that CoffeeScript still produces readable, idiomatic JavaScript...?

As of TypeScript 1.8(?) you can set an "allowJs: true" flag in tsconfig.json, which tells TypeScript to include JS files in your build.

Then you can just manually add type annotations and ES2015/2016 goodness to your code and change the suffix to '.ts' on a file-by-file approach.

I'm doing this at the moment with a fairly large AngularJS 1.5 project, using Webpack with awesome-typescript-loader as the build system, and it's working perfectly so far.