Ideally, convince the client to use soap. It's still the world standard in webservices, and offers a number of advantages to restful services (validation, parseable service descriptions, industry support).
Two alternatives:
Core API to add a requesthandler:
com.mendix.core.Core.addRequestHandler("/mypath", new MyImplementedRequestHandler())
(can't help you with the rest of the implementation though, that's a little more complicated)