Would toggle bolts work? You drill a hole through the marble and a bolt with "wings", spring loaded flanges, pops through the hole. The wings open up behind the drywall and you tighten the bracket down. A stud would be nice though. There is most likely a stud in the middle of your two outlets. A best guess would put other studs 16 inches on either side. If you can sneak a small drill bit or nail between the tiles you could check for studs. But I don't think the toggles would pull the drywall and tile down.
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