As the title suggests, I am looking for somewhere that can make me a custom engraved, wooden, engagement ring box. Any suggestions on where I would be able to do this, or anyone have a laser cutter that could help me make one?

Not sure if I understand your query. Are you looking for a wood-worker who does one for you or do you want a workshop where someone helps you to creat own on your own?

If you want to someone else to do the work look for a Schreiner.

No no, the box is not the problem, I am struggling to find someone to do the engraving on the box with a laser cutter.

Something like the attached.

Sorry, I should have been more clear.

Attached Images

 

A quick google for "Holz Gravur Gravieren" should come up with several options. No personal recommendations from my part though.