Unless you can find a donor bike with a 3sp + coaster brake, then you'll be stuck buying a new hub, if you can find one. My preference would be a Shimano hub, but if you were going that way I would go for an 8 speed rather than a 3 speed... the function is the same, just more suitable for varying road steepness, and I believe you can get the 8 speed with a coaster brake.

Although I did see an online vendor with a $59 price on a Shimano Nexus Inter-3 with a coaster brake... that's pretty affordable. None in stock, though. https://www.universalcycles.com/shop...&category=2713
And here's an 8 speed version (also not in stock): https://www.universalcycles.com/shop...&category=2713

My advice is, don't be shy about sourcing and quoting a price you think might be a little high. You never know what a customer will agree to pay if you can fulfill their unique requirements.
For instance, if you can get a hub + hardware/shifter + rim + spokes for $400, and charge ~$600 (100 for wheel build, 100 for the surgery to adapt to customer's bike + time spent sourcing and ordering- your time is valuable), maybe he'll bite. Otherwise he's just waiting for you to scrounge stull out of the bin so he doesn't have to.