Bad things happen to good people. Young people in particular make mistakes through a lack of maturity, peer pressure, and just plain bad decisions. Unfortunately, felons are not a protected class. A landlord has the right to refuse to lease to a person convicted of a felony.
As an experienced Houston Realtor who has advised landlords and tenants. I tell prospects wanting to lease to reveal everything. Virtually every landlord today runs a criminal background check as part of the lease application process. You cannot change the past or the laws allowing landlords to be able to refuse rentals to people having a felony. You can write a letter of explanation explaining the circumstances and how you have lived your life since.
You might include a picture of the family with the letter of explanation. This lets the landlord know you are responsible now and you have a family to think about before doing anything rash. A list of your achievements and charities you serve could be attached. What you want to do is give the landlord a reason to look past the mistakes of your past. And judge you for the person you have become. If you can sway the landlord with your explanation then the lease application will be judged on your ability to pay, credit worthiness, and terms of the lease.