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Location: Lewiston, NY
Hard to tell but I'd guess it's mahogany judging by both the color and style. Almost certainly if it's old stuff. So if you want to replicate both the color and grain you need to start with mahogany, or whatever wood it is or is the closest you can get to it. In any case, it's a lot easier to start with a darker wood than something like maple, for example. Let's say you use mahogany.
Now you need to really look at it. Can you see dye or stain, or both, on the underside of the edges/bottom, or does it look like it was finished with some kind of clear or colored topcoat. It's not that hard to tell if you study it. Also, was the grain filled? Probably, and often with a colored filler. I've seen black filler frequently used, sometimes followed by a pinkish/orange glaze. High end furniture often had a many layered process to unify the color and to build depth. Jeff Jewitt has a good article in FWW and I think on his website about finishing mahogany.
Once you have an idea of how it was done it's time to start making specimens from scrap wood from the project. This can be a fairly easy but often long and laborious process. No matter, it's imperative you keep meticulous notes as you go so you can go back and compare one specimen from another. Don't be afriad to change directions completely if your first one or two ideas fails miserably. Eventually, you'll find a path and if you keep working at it you should be able to get really, really close.
To do a finish like that my estimate would include probably 30% of the total labor for finishing, and lots of supplies while I figured it out.
John