Don't let guilt, or other emotional reasons, get in your way. They contacted you, they want to hire you. Pay yourself a living wage. Based on your past experience, how many hours will you likely invest in this project? (Don't cheat yourself one single minute. And don't forget shop supplies and finishing time.)
For me, I'd build my price on that time estimate multipled by the hourly rate of what it costs my day job employer (civil service) to employ me, which is my hourly gross salary plus all the other employment costs. That could easily be $80/hour or more. Before you even dive in and start discussing their expectations, let them know how you develop your final bid. Let them hear what is involved, the time commitment, your shop expenses, what it takes to equip your shop to do this kind of work. They should clearly understand you don't sit on a stool with a whittling knife and sandpaper, listening to the ball game on the radio, and an hour later handing them a masterpiece. Because I can assure you, that is their preconceived perception of what you'll be doing.
"Oh, come now, Steve, how could you possibly charge that much?" What is your time worth to you? What are the risks you are taking on in turning a one-off project from a one-off piece of material, neither of which benefit you in the end except financially? What happens when, or if, you are deep into this project and something happens and that piece of wood comes apart, unsalvagable? They need to be plainly and clearly aware before you say yes that it could happen. Will you still charge them if, after a couple hours of time, disaster strikes (hopefully only to the wood and not your body)?
Time x rate = total $. To protect yourself, get half of that total up front as a non-refundable deposit, the rest due at completion, and don't hand it over until the cash is in hand. For this project, you're a business operator first, and a craftsman/artist second.
What if they say no? (They'll probably be shocked at first, then lean towards saying no.) Yep, you'll feel bad, you'll immediately feel like you'll cut that price in half just to make them happy, so you don't feel guilty. DON'T DO IT! If they say no, thank them for the opportunity to bid the job and walk away, let them try to find someone else.
What does it cost to bring a skilled tradesperson to your house to fix the plumbing or wiring? Don't give away your time. Be fair to them, but be fair to yourself, first.
