If you do need the paid version, Tacit Dynamics (tacit.dk) apparently has it available through Amazon.com and through AndroidPit.com as well if either of those will work for you. The drawback of either is that I believe (as with most competing app markets) you have to keep that app market installed on your device.
If that doesn't do the trick, I find that my tablet running Cyanogenmod 10.1.3 has rsync 3.0.7, but I've also installed extra bits and pieces ("Android Terminal Emulator" by Jack Palevich, "Terminal IDE" by Spartacus Rex, "Busybox Pro" by Stephen (stericson)) so I'm not 100% sure that it was originally available. You may be able to script and schedule something of your own based on scripts you use elsewhere, though with a few changes (e.g. "jping" instead of "ping", see Issue 29 on Terminal IDE's code.google.com page though that indicates that it may be fixed).
There's also a "lite" version, which only allows 2 accounts, no Tasker support and no sync filters (which I've never fiddled with anyway, so may not be that important).
Copilot is free to use on weekends (their "day pass" pricing is $5 on weekdays and free on weekends).
I also saw it quoted elsewhere originally, so I didn't see the headline at the top.
Until there's more details out there, to my viewpoint in the upper Midwest this is more a "Jerry Springer Show" scenario going too far and less a "killed him for texting" situation.