Like Neustache, I had to convert a renter to cash, and much preferred it to the cheque bouncing dance that was going on.
It was not a great rent situation, but as long as they paid, we decided put put up with it until the year lease was up.
Even better would have been to have them deposit it to our bank account... and I would have been willing to set up an account at their very own branch to make it convenient for them, too. Just note that the bank will reverse funds if it shows up as XX deposit and envelope is empty or counterfeit (ATM deposit). You can't rely on the funds for the first 5 days until it all clears.
Cash worked a lot better in this case. (half a duplex in SFR area, rented to family).
I think what happened is that they had a garnishment on the chequing account, and did not want to keep much money in there. Yep, red flag. I know other valid businesses, like carpentry repair, that accept cash for a discount, so they can choose what to report for taxation... so they have a lot of mostly valid cash on hand. It is distressingly common here that 20% of one's business may be in cash for this reason.
Problems --
1) Counterfeit is a minor concern. More likely that they unknowingly accepted counterfeit and are passing it on, if they do a lot of business in cash.
2) Counting. You need to count on the spot, then I recommend handing over a receipt slip when you pick it up, using the generic receipt book that has carbon copies.
3) You need to coordinate meeting up with the tenant. Could get the run around for a couple of days and waste your time.
4) Our tenant had a grown son steal their rent cash from their wallet one month.
PROS
On the plus side, you get a lot of face time with tenant, and get to see the outside of the property frequently, they know you come around, and sometimes you get invited into the front hall. Nice to check on things.
These tenants were actually very handy, they wanted to repair the small deck, and we purchased materials, and they did a fantastic job. Practically rebuilt the whole thing. Solidly, too.