I didn't know they even tried to declare independence. They would probably be absorbed by the Republic of the Yucatan after a short period of time.
Actually, it was a lot likelier that it would be other way around. When Yucatan declared independence, the local Spanish-speakers faced two problems: having to hold off Mexico and having to figure out who is the local boss. To make the long story short, they armed the Mayans - which turned out to be a dreadful mistake.
The Mayans rebelled, and soon almost all of the peninsula was in their hands. The only major exceptions were the (wall-enclosed) city of Campeche (because of the fortifications that city was fairly safe) and the capital city of Merida with its port (these were getting ready to run: at some point in Merida they were ringing the church bells and preparing evacuation away from the peninsula).
A temporary respite was provided by the harvest season - the Mayan attack stopped. The Yucatecans were desperately searching for somebody to take them - US, Spain, England, anyone. Nobody wanted to get into the mess, so, in desperation, they asked Mexico to take them back. Mexico sent in sufficient troups to protect them and to take the bulk of the populated area back.
The Mayans kept hold of the less fertile Eastern chunk of the Yucatan (roughly the modern state of Quintana Roo, though without the Mexican-conrolled islands), De facto, they continued holding it for the next 60 years. The unrecognized statelet, which had its capital a Chan Santa Cruz (these days it is called Felipe Carillo Puerto), was only definitively retaken by Mexico in the early 20th century.