Caveat - it's been a while since I've done any "real" networking, so I'm rusty. Also, you're not saying precisely where the devices hook in there, whether they're wired or wireless, etc. But I'm assuming this...
[Cable Modem] --> #1[DIR-655] -> [My Switch] ==> #2[DIR-655] --> [Renters' Switch]
| | | |
Your WiFi Your Enet Renter Wifi Renter Enet
(IPs from #1) (IPs from #2)
I've indicated '==>' where I think you want the network segmented.
If it turns out you need the devices on [Renters' Switch] to also access *your* LAN, then I think what you want is nearly impossible without hooking [Renters' Switch] directly to [My Switch] (that probably means running two cables)
Now, assuming you do NOT need that... you'll still possibly run into issues with "double NAT." But with some "fiddling" I think it would work, at least for casual protection. It won't stop a determined attacker who, for instance, might unplug the #2 DIR-655 and replace it with their laptop - and spoofs its MAC. Even if you glue the connector in they might cut the cable and crimp their own RJ-45 on.

Really, I think the ideal way to solve this robustly would be if [My Switch] supported port-based access controls. (VLANs, or whatever) But unless things have changed, I wouldn't expect that in consumer-level switches.
Other opinions might differ, and YMMV. But hope this helps some.