Use a Co-Signor
Having a co-signor with good credit will immediately get you a pass from the risk department. If the merchant account provider knows that they have a second party on file that has good credit, they'll be willing to accept your application.

If you do get a co-signor, then just look through my comparison page and find a top rated processor that suits your needs.

Find a Specialist
If you can't find a co-signor then go with a company like Durango Merchant Services. They focus on high risk merchant accounts, so bad credit is not a problem for them. Chances are, they'll approve you.

You can also Google "bad credit merchant account" and find plenty of providers. Just make sure they're reputable.

Use a Third-Party Provider
Services like Paypal offer third-party payment processing, where they handle the entire transaction on their end. That alleviates some liability for them, so in most cases, they don't even run your credit.

Offer a Rolling Reserve
Tell the processor that you're willing to leave a "reserve" of funds with them for a while just to cover them in case you default. Of course, this will only work if you can afford it.

Offer an ACH Delay
An ACH delay is basically a delay in the deposit of processing funds to your bank account. The processor withholds your funds for a few extra days as a guarantee that all of your transactions are legit.