Easiest way to change side buttons (or any other button in that matter) behaviour for logitech m570 trackball mouse under linux is xbindkeys.
Unfortunately this package is not available for centos 7 ( i do not know why or if its replaced with another mechanism ) google search return absolutely no results.
So to get around this problem you have to install :
These are fedora 19 packages but works under centos 7. You can not install fedora 20 or 21 packages as they require libpng16.so.16 and that package is not available under centos as well
After you install above packages create .xbindkeysrc file under your home directory and paste below lines:
"xte 'key Page_Up'" b:9 "xte 'key Page_Down'" b:8
now start xbindkeys
[bakim@marko ~]$ xbindkeys
and test your mouse your side keys will act as key up and key down
Also with this setup side keys will act as back and forward button in firefox if you click them while you are holding scroll wheel.
Some useful xte key codes, this keys are case sensitive:
Home Left Up Right Down Page_Up Page_Down End Return BackSpace Tab Escape Delete Shift_L Shift_R Control_L Control_R Meta_L Meta_R Alt_L Alt_R