Its non-trivial, but you could run your own caching nameserver with your onw zone set up for Youtube. (There are a few ways to do this, if your router supports dd-wrt thats a good first step. You will either want to ensure you can use a different nameserver and he can't or go all in and do split DNS based on your IP !).
That said, instead of trying to prevent him watching Youtube, why not get to the root of the problem - his bandwidth usage. If you can get dd-wrt (or your router has QoS) built into it, put him in a lower priority bandwidth pool. This solves the class of problem, rather then encouraging him to switch to another streaming service.