Unfortunately, there's a huge gap between "single container" and "multiple, co-dependent containers". It's a far cry between services hosting a single container and ones offering to host entire stacks.
Right, I wasn't suggesting you could deploy with Docker Compose on fly.io. Hence why I prefaced my suggestion with "It's not exactly what you're asking for..."
And I think you're exaggerating the "huge gap" there. Fly.io can run multiple docker containers for you. Their docs are great so it wouldn't take much effort to learn how to create an equivalent or better setup that covers everything Docker Compose does (and more).
Unfortunately, there's a huge gap between "single container" and "multiple, co-dependent containers". It's a far cry between services hosting a single container and ones offering to host entire stacks.