The restaurants we tried were: Rockin Java (two times), Rolandi, and Especias. (We wanted to go to Casa Mission too, but just never made it). At Especias and Rolandi, my daughter had grilled fish. At Rockin Java, she had "stuffed spuds" one night, and fish tacos (on corn tortillas) another night. We also ate at the Palancar beach club one lunch, and had delicious grilled chicken kabobs and fresh fruit. We went for a day trip on the Tucon (as sailboat), and the crew prepared grilled chicken for her, and brought corn tortillas specially.
The biggest difficulty was finding tortilla chips at restaurants -- at all of the aforementioned restaurants, the chips were fried in the same oil as items containing gluten, so they were off limits. We did have drinks one afternoon at the No Name bar -- it turns out that the bartender at the associated cigar bar has celiac (and speaks perfect English); he told us that the chips at this bar were indeed fried in separate oil, and he eats them (although, in retrospect, I wonder about this and you might want to do some additional probing before ordering chips.) It was no problem, however, finding bagged corn chips in the stores. I also think that the restaurants and bars really would not mind if someone brought their own chips to have with guacamole, salsa, etc.
I was very impressed by how accommodating everyone was. We had a Spanish language restaurant card, and the waitstaff/ managers was generally very knowledgeable about ingredients and were happy to modify meals if needed. You do need to be particularly careful about tortillas, since many dishes are served with wheat tortillas, rather than corn tortillas; however, restaurants were very happy to make the substitution. Also, as in the US, fried items are usually off limits, because of the cross contamination, and a lot of the "bar food" is fried.
There are two enormous grocery stores in Cozumel (both across the street from El Cantil, our condo). These stores don't have gluten free specialty sections the way you might find in the states or England, although I noticed at the Cheudri that they were carrying rice crackers in the international section that were labeled gluten free (they are an Asian cracker). However, we stocked up on food for breakfast and lunch such as eggs, dairy, peanut butter, fruits, ice cream and snacks such as chips. You can also purchase freshly made corn tortillas (in huge stacks). We had brought some items from home -- a bag of tinkyada pasta, which we did in fact have for dinner one night when we couldn't be bothered to go out, a loaf of Udis bread (which held up remarkably well, considering we froze it before traveling, it thawed, we then froze it at the condo, brought most of it home, and then we refroze it at home), some Justin peanut butter pouches to have on hand on airplane travel days, a box of Nut Thins, a brownie mix (which we didn't end up making) and some gluten free protein bars. Basically, it is very hard to find gluten free baked goods (except corn tortillas) but other than that almost everything else can be found in the local shops. I do always feel a bit anxious going through customs with the food, which you do have to declare. However, since everything we brought was packaged -- and is legal to bring into Mexico -- we were waved through without a problem. (You can't bring in fresh food such as fruit, vegetables or meat.)
We did have a pleasant surprise on the plane trip to Mexico. First, they served meals on the plane -- that was a surprise to me in and of itself! Second, the breakfast was cereal and fruit, which I initially passed on automatically -- then I saw that the cereal was single serving bowls of General Mills gluten free Rice Chex!