You can get umbrella platens for some heat presses that are shaped to the section of the brollie. You can either dye-sub or apply vinyl. I've only ever done a couple with a simple vinyl design but it looked good. I had a pocket platen which worked fine but you need 2 pairs of hands ideally!
We had one sitting there so I thought I'd have a go, personally I have no Market as we don't use brollies here due to the wind, fair bit of messing around yes.