There are some commercial efforts but not much in the open source space which in my opinion is a bug problem because APIs should be fuzzed properly - especially when written with dynamic scripting languages.
Thanks for clarifying this and your info on Burp's capabilities above. What are some of the commercial options you just mentioned? I'm dealing with a large app not written with C but does have API endpoints over http. For a start on some black-box fuzzing, I'm thinking I could use Radamsa's client/server capabilities.