Thank you Håkan, that worked almost out-of-the-box (not only for the JRE but for the JDK, too).
There was a slight problem, "sudo fakeroot" didn't work; the error message was something like "Java setups being executed as root tend to somtimes mess up common settings". Setting up Java as an unpriviledged user on the other hand resulted in some minor problems, basically in not replacing some shared logos/images and (slightly more problematic) WebStart not being installed.
Anyways, Sun Java is up and running!
Thanks Lenard too, I could figure that would work too, and I'll remember it when stepping into other Linux distris lateron. (CentOS BTW is one of my other favorites too.)
- Whew I'm a Linux geek *rofl*