It's tough to find what your looking for because the city, in its infinite wisdom, passed a first come first serve law that requires landlords to rent to the first person who applies and meets all the requirements in the ad. So in response landlords have put very stringent requirements in place since they can't take the risk of having someone apply who isn't a good fit, but who meets the criteria.
It's especially true now with the eviction moratorium in place and likely to be extended and extended. I'd look outside the city limits if you can.