Personally I'm being more ambitious and I plan to force (yes force - as in they have to agree to this upon lease renewal) 100% electronic payments. You can accomplish this with Paylease and any of its integration partner property management firms, or with competitors such as Paynearme (integrates with Appfolio among others).
For the unbanked who refuse to use any technology -> Walmart & Kmart accept their cash. The resident gets a PIN number and thus does not have to be using a smart phone or computer.
For those who prefer checks -> ACH via the resident online portal on phone or computer.
Debit/credit card users -> enter their number in the portal.
This method will let you go 100% electronic without alienating the technophobes in your customer base.