You NEVER have to feel obligated to be available to watch your neighbor’s dog! It is okay to let them know you’re unavailable at certain times.
Keep in mind that you’re not their dog-sitter, you’re simply a Doggy Neighbor that hangs out with the Doggy Owner’s dog from time to time because of your love for dogs. Communicate with them clearly that you won’t be able to hang out with their dog at the time they asked, and if able let them know other alternatives to when you can hang out with their dog.