Making Omeka Restful - literati/plugin-REST GitHub Wiki
From Omeka 1.5, I don't believe there is an easy way to define a REST architecture. By the end of this page, there should be.
4-years old omeka forums post expressing need for the future and no answers
Probably the simplest approach would be to implement the Zend Rest Route and let our controllers extend ZendRestController
In answering an omeka forums question, Jeremy Boggs has pointed to a way forward and posted sample code.
Searching for instances of Jeremy's example within Omeka plugins turns up a very nice example given by Exhibit Builder for defining routes