It depends what your needs are, you haven't given any details. I'm not aware of anything with the JSONBin.io API (frankly I don't like their API, I think it should be more RESTful).
CouchDB is in many ways very similar to JSONBin and self hostable. I have also written small services that use SQLite's JSON support and wrap that up in a fairly restful API (e.g. POST a document to a list adds an item, etc.).
Another option is to use something like PostgREST, which I get isn't at all what you asked, but in this day and age you can just ask ChatGPT to make you a schema and it takes 2 minutes to prototype a REST API.
Really it depends if you have preferences for what datastore you use, as that is the more difficult bit when self hosting.
dontdoxxme•53m ago
CouchDB is in many ways very similar to JSONBin and self hostable. I have also written small services that use SQLite's JSON support and wrap that up in a fairly restful API (e.g. POST a document to a list adds an item, etc.).
Another option is to use something like PostgREST, which I get isn't at all what you asked, but in this day and age you can just ask ChatGPT to make you a schema and it takes 2 minutes to prototype a REST API.
Really it depends if you have preferences for what datastore you use, as that is the more difficult bit when self hosting.