I am having a semi-local Amish place make me a completely different seat for my cart. I would also try the auto upholstery places, if they are good at what they do, they should be able to do something like that.
There are many Amish shops that could/would do that for you but most don't have websites.
What state are you in? That helps with giving you ideas/phone numbers & addresses.
Also, you could check with many of the cart selling websites - they may have the contact info for whom built their carts and you can then get in contact with them. What type of cart do you have?