True, anything should be OK but it will be a little strange if you run three speakers and a sub off a fourth channel...
I'd divide the amp up 50/50. Run your front and rear left speakers off of one channel, the front and rear right off of another channel, and the sub by bridging the third and fourth channel. It won't be optimum sound quality really, since you won't be able to adjust the volume of the rear speakers independently from the front ones, but everything will get hooked up at least.
Another option is to run each front speaker off each of two channels, and run the rears in series in a "tri-mode" fashion. This should be mentioned in the owners manual if it is even an option for you.
If you're running the Rio into another head unit, you might use it's built in amp to power the rear speakers and use the amp for the front and sub?
Check the owners manual anyway, there may be some diagrams in it for recommended setups. Also, whatever you go with, keep an eye on the amp for a while to make sure it doesn't get too hot - if it does, you will need to rethink your hookups.
I know you said you couldn't do it, but another amp is by far the best bet. Perhaps you could sell off the current sub and apply the money towards something like an Infinty Basslink or a Bazooka (self amplified subs), if it's a space or wiring restraint that you have.