This day in time most all property managers will do a credit score check, as well as a criminal background check in order to protect their clients. However, this does not mean that you will automatically be denied. What I recommend is that you speak with the property manager and explain your situation as to why your scores are lower than what they recommend. For example if there was a medical reason, divorce, loss of employment etc. that caused the lower score initially, but that you are now in the process of working to correct. and can show them a good rental history, electric bill, etc that you have been able to pay on time, they will take that into consideration when they speak with their client. However, ask directly if they would recommend it or not before allowing them to run your credit for the application. Try with each real estate company, as each one may have a different procedure that can assist you and if they're procedure doesn't work, don't be afraid to ask them to refer you to another company. Most companies do network together and are willing to help people find a company that can help them.
And last, look to for sale by owners that have had extensive days on market online. Most sites will give you a post date. They may consider the option. Best of luck. Hope this helps.