How hard is it to qualify for a rental home now?

Trying to find a rental home close to our son's preschool and his therapy clinic. How hard is it to get approved for a rental home in the city? I have a small family and decent credit (600+) but still repairing it from 2 years ago. If I make close to 6 figures and have good rental history from an apartment and private landlord can my family get approved?