I've been using DailyRazor to host a private
Tomcat instance for some years now. Mostly I've been a satisfied customer, although occasionally other users seem to do CPU-intensive stuff on the same host as mine, so the load average jacks up and my stuff slows down. And sometimes my email gets rejected because of the IP, when other folks have sent spam from their instances. But those issues are to be expected when you go for a shared setup, I guess, and they haven't been severe enough to drive me away.
Some other Java hosting providers are listed at
https://coderanch.com/wiki/659865/Servlets-Faq#hosting