Is there anywhere I can decorate an elephant as a tourist?
This is certainly an unusual request. Elephants that are decorated this way are usually done so for festive occasions...or for tourists, and the picture that you have used is from Rajasthan. I honestly don't think you'll find elephant decorating as a part of any organised tour! So what I would suggest is, go to Rajasthan, book a tour with elephant rides / find an elephant ride, and negotiate with the handler whether you can do this. Haggle hard! This is such a one-off request they might come across that they will most certainly try to make the most of it.
(Elephants are also found in Kerala, but they won't be decorated this way there.)