Although Romani and Sami languages vary widely from region to region it is difficult to differentiate dialects based on the limited amount of text provided within the songs.
For pre-dissolution of Yugoslavia I assumed the language to be Serbian and not Serbo-Croatian -- if that is not the case, please let me know. Additionally had some trouble telling if Chakavian and Surzhyk should be counted or not.
The song ''Rock me baby'' from group ''Riva'' is sung in croatian by croatian singers. If you ask me accepting serbo-croatian for it would be ok I guess, but croatian should be accepted for sure. Serbian would be incorrect imo.
Don't you count sign language? It has been used in the contest several times, first by Latvia in 2005. (Technically, of course, you don't "sing" in it.)
I did think of Ancient Greek but assumed it would have been contained in "Greek". Perhaps you ought to specify "Modern Greek" when it pops up, to be clear? Ancient Greek is just as much Greek as Modern Greek is, after all.
For pre-dissolution of Yugoslavia I assumed the language to be Serbian and not Serbo-Croatian -- if that is not the case, please let me know. Additionally had some trouble telling if Chakavian and Surzhyk should be counted or not.
Main source:
https://en.wikipedia.org/wiki/List_of_languages_in_the_Eurovision_Song_Contest