Substitute for coconut in macaroons
You're right in that you don't want to use oats or flour.  Your best alternative is some other form of ground nut.  Almond was actually the original macaroon, with coconut coming later.

Rather than trying to modify the recipe directly, I'd recommend searching specifically for an 'almond macaroon' or 'amaretti' recipe.  Beware of 'macaron' recipes, which is the spelling the French use; it'll work, but they're typically intended as two halves of a sandwich cookie.