Be prepared to show your credit report anyway and to explain why the score is low. If you can show a recent history of paying your bills on time even though you may have struggled in the past that should go a long way. Have proof of income ready to show you can afford the rent. You may want to also have a criminal background check and an eviction history done to show you are a law abiding citizen and have never been evicted before. Get personal written references, from former landlords if at all possible, otherwise from friends and associates. Offer to set up direct deposit for the rent from your bank account to the owners account. And, finally, offer to pay both the first months' and the last months' rent in advance. That way the owner will have a 'cushion' of one months' rent should you default on the lease agreement.
Good Luck, I know it's not easy in this kind of situation but you will find the right place if you persevere.