I don't think you would ever get a court to support holding a security deposit because you have to repaint and clean a carpet.

My client said that he would pay full price at closing so a deposit was not necessary.

Buy and hold type property where the government direct deposits your payment once a year in arrears. 1/2 mile highway frontage on the west, and 1 mile of county gravel road frontage on the east.

In that case, what do you do in the deposit section?

Or money orders that now I have to take a trip to the bank to deposit.

Because of the very low vacancy, the ease of getting security deposits and good collections, I kept that property longer than any other, 18 or so years I think, cash flow was great as we had a base rent then additional amounts for each additional occupant

Meanwhile regarding deposit payment, it's attached to purchase contract and hold by escrow company or real estate attorney (different states have different rules), for example in Manhattan or other part of New York State, for up to 1 million dollar property it's reasonable $5,000, for Los Angeles 3% of sale price.

One drawback is that they are paper-based, not online, so it's checks to deposit and paper records.

If a tenant wants to have a dog in the property, I charge a higher deposit and a higher rent. 

I would require a pet deposit.