It was the Cozumel Humane Society. Feel free to contact them first, but the last two times we visited we just dropped in. I'll link the volunteer page. They also have an album on their social media page called "Give us a Paw" that has wish list items for donation. If you are docking at the International Terminal or Puerta Maya, the shelter is about a 15 minute walk or a short taxi ride.
https://www.humanecozumel.org/voluntariado?lang=en