We started before some of the electronic methods of rent collection and communication were around. 

The majority of the section 8 rent comes in from the city electronically like clockwork leaving a small portion for the recipients to pay.  

I previously used an electronic service but they charged almost $10/month.

I wasn't sure what I was missing, but I don't consider being forced online a flaw - if my tenants aren't savvy enough to apply online, they probably aren't savvy enough to look at our listing, pay electronically, communicate by text, etc.

As part of the lease agreement, there is a clause in the lease authorizing him to withdraw the rent as at when due.In fact, the clause on my lease is something like this:AUTOMATIC ELECTRONIC PAYMENT AUTHORIZATION: Tenant authorizes <OWNER> to initiate, and Tenant's financial institution to honor, an electronic funds transfer payment in the amount of the rent from Tenant's bank account effective on the first day of each month.

Why not have him pay rent electronically (using PayPal's free option or one of the many other free/cheap options)?

In order to continue with this online application, you'll need to review the Application Agreement carefully and acknowledge that you accept its terms.1) Signing this application (electronic or otherwise) indicates that applicant has had the opportunity to review landlords tenant selection criteria, which is listed above and available upon request.

I personally wouldn't want to accept cash because I would like an electronic paper trail of sorts. 

Cash payments can't be tracked easily and  electronic payment options are plentiful -all you need is an email.

You can apply, complete a lease, sign the lease and pay the deposit all electronically.