Hi, Alfred. Some places will work with you on a case by case basis, especially smaller landlords. The best thing to do is be honest about it, and explain what happened, because there is a chance that the place you move will run an eviction report. Most applications will ask if you have any evictions, but it is not an automatic disqualifier for all property managers and lawyers.
With a co-applicant, co-signer or both there is a good chance you might be able to get into a place. They may ask for a co-signer or co-applicant that has the ability to cover the rent with their own income. Some places may legally be allowed to ask for a larger deposit, but this can vary by state and city jurisdictions. Large apartment complexes might be more stringent than an everyday landlord that is just renting out an old house of theirs.
Some places are more compassionate than others, and not all of them operate on robotic principles.