I don't think so. There's a big difference between a single signal with 2-4 views included and two separate signals that allows you to send each one to separate TVs or monitors. Minecraft (and the consoles) don't make 2 separate signals.
The only thing I can think of that might work (big "might") is to use a splitter so you send that one output signal to both devices. You'll still run into the "now it's fuzzy to see" problem. (To be honest, I never could get my monitor to work).
Break down and get an HDTV (when you can afford it). Everything will look better and you'll be glad you did. (You'll have to eventually anyway).
Bleh, yeah, I know. I really should. But I am living dollar to dollar at the moment and the $20 I splurged on Minecraft was kind of a big deal to begin with haha. It just sucks because a friend let us play his on the PC and we were having a blast together. Then we go and buy the PS3 version thinking we can play it at home annnddd... $20 down the drain. Shoulda just went with the PC version...
The Meaning of Life, the Universe, and Everything.
If you guys live apart, and you each have a PS3, you can play online. There is no way you can play like that on a STD TV with split-screen. The only way I can see something similar is on the PS Display IF this game decides to support that dual screen gimmick with the 3D glasses.