You can find written Rajasthani in Devanagri on the Internet. There aren't many good websites though, as most Rajasthanis are bilingual in Hindi and don't care much about reading or writing Rajasthani. And by the way, there is no unique Rajasthani language. There are a group of related dialects which are collectively called Rajasthani. Linguistically, Marwari, Mewari, Godwari etc will be the proper name of any given Rajasthani language.
It is the Muriya script question which really piqued my interest . After a google search didn't give any useful results, I searched some alternate spellings, and a search of "Modiya script" brought up some good results. Apparently it was a script used by Marwari merchants in the years past. Now it is pretty much dead.
Also interested in knowing if this Modiya script is really the same as Modi script of Peshwa empire, the fabled secret script?
So some more research reveals that Muriya/Modiya/Mahajani is one and the same thing. And apparently the script was important enough for Unicode Consortium to take the trouble of compiling a standard version of the script and reserve a block of characters for it.
Following link gives a good overview of the history of the script, and the process regarding the Unicode standardization of script. This document also has some good handwritten examples of the script.