Have you looked into CircleCI?
[1] I did also ask about selfhosted stuff, but I'm not willing to host Jenkins for myself. I've heard nothing but complaints about managing a Jenkins install. It's been fine as a user (if a bit confusing), but I really don't want to admin it.
My current gripe is that there doesn't seem to be any way to declare that one pipeline depends on another, though I may just be missing something in the docs.
What I'm trying to do is have my front-end feature branch builds run against the build of matching back-end branch, but there doesn't seem a way to declare "this build should depends on the output artifact of that build".
I don't really want to have to wire it up myself using their API.