puppy linux may be an option.
my laptop has 32mb ram pre-installed and a slot in the back where you can add more ram. i have an additional 64mb in that slot and have knoppix 5.1 harddrive installed with swap function enabled . all systems go as far as i can tell so far .KDE desktop and openoffice are both running fine.
have installed a new hard drive of 20 gig replacing the original 4 gig.
2gig seems just t o small to me.
maybe you can run your swap partition on an USB external hard drive or USB flash drive to give you more usage of your 2 gig..