Via SSH, this should do it: apt update && apt install rsyslog
BUT, if it's collecting a lot of information, you may need to move it to the /apps directory (which resides on the data volume) instead of on the size-limited OS partition to keep from filling up the OS partition. That's done by creating a directory in apps, moving the content of the program directory into that new one, and replacing the original directory with a link to the new one. Alternately or additionally, you could also change the location of the logs to somewhere on the data volume, if that's configurable. Putting the logs somewhere you can access them without logging in as admin may also make sense.
I'm not actually running it, but I looked at the list of dependancies and didn't see anything that looked like an issue. As I said, the main risk is that you collect too much with it and it goes to the default /var/logs, which is on the OS partition. The ReadyNAS OS partition is quite small, and filling it up, or even approaching full, can have bad consequences. App versions developed expressly for the ReadyNAS should take care of that, but standard Debian packages typically will not.
