Which product are you using? Dynamic C 10 includes a "Remote Program Update" library that supports multiple methods for delivering firmware updates to some of the Rabbit 4000/5000 and all Rabbit 6000 devices. There are sample programs for TFTP, FTP and HTTP client, along with one where the Rabbit is an HTTP server that accepts firmware updates.
Read AN421 (http://ftp1.digi.com/support/documentation/022-0144_C.pdf) for a description of the feature, or look at the files in Samples/RemoteProgramUpdate.
You might be able to use Scott Henion's code for Rabbit 2000/3000 products, but it isn't trivial to incorporate it into your code, and I'm not sure if he's still selling/licensing it: https://shdesigns.org/rabbit/st-download.shtml