PHP REST API
No ready-made situation, we've done a few custom things.
Basically, you want to think about the minimal amount of access you need (read/write/tables/etc).
Mirroring all the access levels and security of the CMSB would be the most work. Because the underlying database is MySQL any generic MySQL REST API would work, but you need to think about security and how you're going to limit who can edit what.
Hope that helps! If there's any other questions or a specific project that you want help on feel free to contact us.