After watching someone make a newspaper pot on one of those expensive wooden forms, I eventually worked out this similar method for making newspaper pots.
Note: Whatever can you use, make sure it has a concave (indented) base. Make sure your hard disc, whatever you choose, can sit inside the dent comfortably both in width and in height. If your disc is too tall so the rim of the can doesn't go down to the table/worksurface, you won't get as good of a crimp and your pot will not stand up very straight. If you are stuffing lots of the pots in a tray, this probably doesn't matter.
Roll your strip of paper tightly and evenly around the can.
Place your thumb securely on the end of the paper on the can
Fold in the end "seam" first
Then the sides...
Then the opposite side to the seam side
Place your film canister top/coin/button/disc on a flat surface. I'm using the floor here but a table should work equally well.
With the paper still on the can, position the can over the film top/disc and press down. You can twist the can around a little too (within the paper, don't twist the paper!)
Remove the can from the film canister top/disc and slide the paper pot off.