The black fingerboards on most guitars are made of a wood called ebony. Expect it to cost around $350 - $500 dollars to get it done right. If it costs less then that, don't let the person do it. This is a major job, which includes removing the fingerboard (and I won't even tell you how to do that, as it is a difficult job which requires experience), cleaning up the glue joint, making a new fingerboard (which takes us about two hours in and of itself, and we are highly automated for this task), and reglueing the fingerboard VERY precisely. Then we have to fix the finish around the fingerboard, which is a particular pain in the ass on the matte finish Martins, and will never look perfect as the finish is a catalyzed urethane. If it was nitrocellulose lacquer like the high end Martins, it could be made perfect, but not the low end ones.
You can also expect the turnaround time to be somewhere between three and six months.
In short, get a new guitar if it matters that much, or better yet, learn to like rosewood fingerboards (which look really cool).
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