All these States have a Deferred Adjudication - type of law but they all call it something different.
In New Mexico, they use a term for their Deferred Felonies that I think describes the situation even better: Conditional Dismissal.
Oklahoma calls their deferred felony situation a similar name - a Deferred Sentence.
Arkansas is one of the few states to convict for a deferred felony then upon completion of the probation, they "un-convict" - they call this a First Offender Sentence.
The good news is that I have apartments in Houston, the DFW Metroplex, Austin and San Antonio that will work with your Deferred Felony, no matter where you "got it" and whatever it is called.