The Fair Debt Collection Practices Act is a federal law, not an Arizona law. Arizona may have state laws that apply, and I cannot speak to those.
As far as I know, there is no law that forces a debt collector to accept a payment arrangement, although they have to give you credit for any payments you do make.
If you do get a collector to agree to a payment arrangement, make sure they promise to stop collecting as long as you are making payments, including a promise not to sue.
Before you do so, however, you should request validation of the debt. Often, debt collectors have only a name, phone number, and a few other bits of information. You should make sure a debt is yours before you pay it.
Lastly, you should contact a consumer lawyer in your state. The NACA lawyer database is a great place to find one who will be able to help you understand your options.