I'd second afraid.org, have been using them for years and they've always been great. They also support dynamic DNS so if you're on a dynamic IP address you can have the address be updated automatically when your IP address does.
More relevant to the question, I'm pretty sure you can create NS records for a subdomain as well. I was experimenting once a few years back with a DNS tunnel service and was able to get the DNS side of it configured. Never did get the service itself working but it was more of a curiosity at the time so didn't spend a massive amount of time on it.