Get a cosigner who has a good credit history. Note that the cosigner becomes equally responsible for the rental payments and other charges. Check your credit report for inaccuracies so that the landlord has an accurate picture of your credit history. Don't be late with or skip out on rental payments. It will come back to haunt you.
Landlords have credit bureaus that share information about tenants' payment histories.
Rent through a private landlord, rather than a large rental agency. They sometimes have less restrictive policies. Be sure to have character references ready. Try a fixer upper. Offer to trade your sweat equity for a reduction in the rent or deposit.