Have you looked at the Easterbunz side-snap trainer, or the Wee Weka side snap diaper? There are links to both patterns in the sticky

You might be able to just lay the pattern on the prefold (although you might need premium or toddler size prefolds for them to be big enough) and then bind and elasticize the cut prefold edges with FOE to keep them from fraying. Then just add your choice of snaps or H&L, and voila! A side-snapping non-waterproof trainer pant

You don't have to use a diaper pattern for one specific thing--if you have a side-snapping cover pattern that you like, you can always make it out of absorbent material to get a side-snapping fitted. You might need to take off 1/4 or 1/2 inch all around to get it to fit in the cover, but if you make the cover from a knit, stretchy material (like fleece) and the fitted from a woven, non-stretchy material (like twill or flannel) then you can usually just leave the pattern unaltered
