Isn't Coleman made by Cal Spa? Probably a long shot, but you could try quickspaparts.com (they are the Cal Spa parts outlet), or maybe give Calspa or Coleman (or whoever is their parts dealer) a call and see if you can get ahold tech support, or someone who cares. Manufacturers always have boxes of old crap laying around in a dark corner somewhere, the hard part is finding someone who cares enough to go pilfer through a bunch of old dusty boxes to find what you need. Need to find an intern or new person on the todem pole who has the time. I bet dollars for doughnuts there's a couple stuffed in a box somewhere at the plant. I called on lots of different mfgrs for years and I've seen old boxes stuffed full of ancient old product first hand at factories. Might also find a list of dealers in your area and beyond and see if they have some used Coleman stuff laying around.
Otherwise check as many hot tub parts places online you can. Look for your tub's model number and plug that into searches. Look on the controller for a part number if you can. If you find something new, chances are it will be a lot of money ...maybe more than you're willing to invest into your old hot tub, who knows? Also, keep an eye on Ebay, or maybe maybe do a SearchTempest (regional or national craigslist search) and see if you can zero into come controls from a tub kept indoors. Another idea is, you could take a picture and measurements of the controls to a sign printing place and see how much it would cost to design and print an adhesive label to look the same as the original controls label. From a design perspective it should be pretty easy and truthfully, if you figure all the time you might spend searching on the internet for a used controller, or the cost of new ...if you 'do' happen to find one, it might be the cheapest way to go to have one printed. Once they make one, have them save the design and they can print another later on if the chemicals don't play well with the adhesive. Or, have them print 3x and sell the other two on Ebay to help defray your design costs.
Or, if you have kids, how about buying them a silkscreening kit and challenging them to make a silkscreen and re-print your own face plate. It might not be perfect, but it could be neat and custom. Probably a hundred youtube videos out there on how to do it and probably a way to make silkscreen lettering look near perfect using some low-buck but unique idea. Or, a sign making shop could cut the silkscreen lettering professionally too using their plotter and have your kids do the paint screening. Heck, there might be places out there that even re-print out labels. If you know some gal who's heavy into scrapbooking they usually have a lot of stamping things and and could let them have a go at trying to redo the lettering with their stamp kit. They can usually make up whatever is needed.
Lots of ideas there. Good luck!