Try www.carecredit.com You can make credit arrangements through them.
Never tell a vet up front that you can't pay. Get care for the dog, and then make the arrangements afterwards. They won't rebreak the leg and send you on your way, they'll be forced to work with you.
But don't stiff them on the bill; it is your responsibility to pay, and your responsibility to provide care for a suffering animal.
We have a credit card that we keep hidden away, with a zero balance. It is for unexpected vet bills only. That way, we are never in the situation of having to make a difficult choice.
Years and years ago (before we came up with the CC strategy) we had a dog with a severe bowel obstruction. We obviously couldn't shell out the $2000 on the spot for his surgery and critical care. But we went ahead with the surgery, and when it came time to pay, then we said we'd have to make arrangements. They were not happy, but did allow us to leave post dated checks that they would deposit every month until the balance was paid off. We made darn sure that the checks would go through, and paid off our debt in a year. Then we got the CC so we would never be in that spot again.
use a credit card and make payments there. there is also insurance for dogs you may want to sign up for. wont help you now but will help you later. having pets is like a child. you wouldnt let your child suffer would you? Im sorry to hear about your dog. perhaps your sister will pay for some of the bill?