There is no actual way to play runescape on your PSP, only cheap workarounds.
I'm sure you've heard of VNC, if not, I'll tell you. It's a remote control software used to control computers over a network. It's open source, so it's constantly being developed for newer and better needs. Where does this tie into your runescape and PSP?
PVNC.
You run a program on your computer while it's logged into runescape, then you run PVNC on your PSP. Using your PSP, you control your computer, and play runescape as if you were playing on your PSP.
At this time, I can't find the download link for PVNC, so you'll have to find it on your own. With the download, should be an instruction file telling you how to use your computer with your PSP.