I'm not sure about credit but I know you have to be in pretty good standings with VZW. I believe at least 6 months or more without any interruption in service or late payments. You can read below for Verizon's stance on EDGE or check all of the FAQ using the link below...
I'm an existing Verizon Wireless customer and received a letter about not being eligible or having to make a down payment for Verizon Edge. How can I become eligible?
Because Verizon Edge is an installment agreement to pay for equipment over time, we check for financial good standing on any account in your name. If you're not currently eligible for Verizon Edge, there's a variety of ways to qualify for this type of equipment payment option:
For your convenience, there are several ways to make a payment:
Note: You may also be eligible for Verizon Edge by paying a down payment within the first 6 months of service with Verizon Wireless based on the original activation credit decision when you opened your account.