As far as I know, you can't install packages without being root. The installed files are copied into system directories and the rpm database is updated as well. So you cannot change this behaviour, unless you mess up all the permissions of the directory tree.
Anyway, there is a chance you can extract the files from the RPM and install (that is copy) them somewhere into your home directory:
Code:
$ rpm2cpio AdbeRdr9.1.0-1_i486linux_enu.rpm | cpio -dimv
Then add the directory containing the newly installed executable to the PATH, being sure it comes before the directory where the current acroread executable is installed (usually /usr/bin). This is because the system look for executables (commands) inside the directories specified in PATH, following the order as they appear. The first executable encountered is that one executed.
Code:
$ export PATH=$HOME/opt/Adobe/Reader9/bin:$PATH