Can I pay a deposit and pay the balance off monthly I don't have the money now

If for vet services I believe they accept a form of credit for animal care. You'll need to apply for that credit.

They do care credit l believe which allows for monthly payments

Not sure Call them

Is this for a veterinary service?. If so maybe yes. If it's to adopt I would say no

Call the office. I doubt it. When I adopted my dog they asked for all the money up front.