Much will depend on the individual landlord; therefore consider being upfront as to why your credit may be amiss; do show proof of employment/pay stubs, have some reference letters handy, etc., and go from there.
Best to find individual owners who rent properties and that you can talk with one on one. Apartments owned by major corporate players are a black/white analysis and you won't make it. Individual owners value the face-to-face interaction and if you can explain the situation in a way they can understand, you might get an approval. Offer to double the deposit is another way to win out. Good Luck!