It's unfortunate that a few bad apples have spoiled the credit system for so many others. We used to allow payment plans but in the last few years every single person who we offered a payment plan to defaulted on us! So, now we have a no credit policy.
If you are phoning around asking for a payment plan, I have the following advice. See if you can borrow a small amount of money from someone so that you can at least pay something for the visit. If you call a vet's office and say, "I would like to set up a payment plan and I can start off by giving you $100 today and then $100 a month" they are more likely to consider you than saying, "I have no money, can you help me."