The in game announcement that stated that May 31st was the last day for the Emerald Dragon also mentioned that the Pearl Dragon would be the gem dragon for the month of June. How do you breed a Pearl dragon? What incubation time indicates that you got it?
It appears the first and probably only combination is Snow and Seaweed dragons as per the Dragonvale Wiki. Note there was only one combination for the last gemstone dragon so I wouldn't try other pairings. The Pearl Dragon incubation time is 30 hours; since no other dragon has a 30 hour incubation time you'll know you got it just by the time.
Remember you can not breed gem dragons with any other dragons. Even if you have two Pearl dragons they can't breed with eachother.
Looks like it can be bred already; it's in the Market and people are already reporting successful breedings and there are already egg pics:
Their breeding time has been confirmed to be 30 hours matching the days of the month, same as the Emerald dragon. It is likely to assume that this gem dragon will also only be breedable during the month of June.