Generally, DME/DME/IRS will meet the requirements for P-RNAV, but you would have to check your aircraft manual to be sure.
If you use DME/DME/IRS and the failure of a DME would affect the service coverage, then there will be a published Critical DME Gap on the chart. Your aircraft's equipment will determine how big that gap can be and still maintain the required RNP.
After a second read of your post, I would clarify my above statement. If the chart says (GNSS) then I would say that you must have a GPS and DME/DME/IRS would not permit you to fly the STAR.