I've seen these flex curve templates before. Never used one, but it seems like it would work here. Just a bendable piece you screw onto wood and use it as a router template. If you want your template to be symmetrical, you could use one of these to make the curve on a piece of scrap, and then use the scrap as a template on each side of this template. You can probably find a cheaper one that this with some searching.
If you’re wondering how you’re going to get the curve on your template to be smooth...consider this: CMT TMP-1200 Flexible Template for Curved and Arched Routing, 15/32 X 15/32-Inch https://www.amazon.com/dp/B008AXXH54/ref=cm_sw_r_cp_api_glc_fabc_48d2Fb43RP3HG?_encoding=UTF8&psc=1
Flexible template might be the way to go. Maybe you can find a way to do something similar but cheaper?