I'm making a wood cheek rest for an Enfield rifle, akin to the old school sniper rifles.  But instead of attaching it with wood screws, I'd like to give it the ability to adjust up/down.

Are there any discrete-but-solid ways to achieve this functionality without spending a bunch of dough?

MPA makes a quick release riser kit for their chassis that should be easily adapted to a stock, you would just need to make 2 hollow tubes to glue into the stock for the riser to slide into...add 2 set screws to the tubes for adjusting...or a couple bushings for the riser to slide down onto to establish riser hight..it runs 35-75 bucks depending on how you want it...

https://masterpiecearms.com/shop/mpa-quick-release-cheek-riser-system/

Their bushing and thumbscrew setup for the above riser...

https://masterpiecearms.com/shop/mpa-cheek-riser-thumb-screw-system/

How readily adjustable do you want it to be?   A very simple approach would be a set of shims between the cheek piece and the stock.  A slightly more adjustable option might be two rods guiding the cheek rest vertical adjustment with the rear rod being captured by a “set screw” coming in from underneath the buttplate.