I've currently got a lot of plasterboard off cuts stashed in a dry corner for mounting targets on, I use either Shoot-n-see 25mm discs, or as Rich noted above, self adhesive 'dots' which are meant for putting prices on things in shops. About 99p for 500 10mm diameter if I remember rightly. I get black ones, presumably so up market outlets write the price in silver ink.
Your problem appears to be that the pellet holes are too ragged for accurate scoring, I would suggest shooting a smaller group on each target, 5 not 10, & use flat nosed pellets which were actually designed to address this issue. Another thing, if the paper is damp it's more prone to tearing so store it somewhere toasty, like the airing cupboard.