Most landlords who work with Realtors will have their agent checking credit reports. Move in costs will usually cost you the first months rent and 1.5 months security deposit.
Private owners do not list their properties on Trulia. You could check out FRBO and other sites. If you have credit issues, you are best to rent from a private owner who usually will not check your credit score, either.
If you wind up looking in Northern Ocean County, I would be happy to help you.