Yes, you can. Look for a realtor that you can trust. Be honest and tell the truth at the beggining. This is going to make a huge different. There are millions of families like you. There are certain things that we can't control, so we need to move forward and do our best.
Show your responsability with your payments, recently. Recommendations and job letter, is good too. If you have the money to pay in advance, good for you, but not everyone can do that, especialy is you lost your past job or house, and you are trying to get in track again. Owners/property managers know when a person is honest (if there are honest too). Offer automatic payment, renter insurance and evidence of your income (job). Plan B: co sign the first year until you have the confidence with the owner. Now are hard times, everyone want to move the economy, let help each other! Good luck and God bless you!