The p3rl.org/Minion job queue has a sqlite backend and I'm aware of it handling what seemed to me a fairly acceptable amount of throughput and the source to https://metacpan.org/pod/Minion::Backend::SQLite looks pretty comfortable to me.

I've not run it myself in production but I would definitely have heard if it went wrong, I think OpenSuSe's OpenQA thing does build worker boxes that way (though of course they'll have fairly slow jobs so it may just be the write throughput doesn't matter).

This being HN, I'd like to point out you can steal the SQL from the source for your own uses if you want to, this just happens to be the example full implementation I'm familiar with.