I would guess that in addition to proper lathe-turned thread spools, sewing thread could also be wound around simple sticks or flat winders made of bone, antler, horn, wood or parchment. Whatever was available and worked, in short. I'd need to check in some books, though; and sewing thread storage items are not a primary interest of archaeology, unfortunately.
None of thes possibilities mentioned, however, are cheap enough today to use for winding thread on to sell (unless, possibly, bought in serious Bulk with a capital B, and that is not suitable for my small-scale business).
I once got myself a box of lollipop sticks from a craftshop to use for heddle sticks. They were about 10 cm long, 0.5 cm in diameter and really cheap. Since I got so many of them I've started winding thread onto them. I tape them to my bobbin winder so I don't have to do it by hand. Maybe that would work for your market stall? It's a little slower and slightly more expensive than winding round a paper core, but a round stick is reasonalbly timeless in appearance...
I have thought about the paper roll problem, and I have a very nice (I think) idea how to solve it - however, because that idea will mean a bit of expenses and pre-planning, I won't go for it this season. If things work out halfway decently with all these bits of string and thread for sale, there will be a different "thread carrier" next summer...