What coin are you planning on using? A dime will be pretty thin, a quarter flattened out may get thin as well. For me, a thin inlay is hard to put in and if it something like a moon with two small points, then it's a bit more difficult. To overcome this, I like to use thicker stock.
When I make an inlay (as opposed to using a store bought one) I fashion the shape out of paper, when I am satisfied with the shape, I place the inlay on the stock to consider how it would look, placement or determine if any alterations need to be made. Once I am satisfied with the paper inlay I trace the paper inlay onto another peice of paper and this one I glue to my metal stock I intend to use for the inlay. I keep the original paper inlay as a backup in case I need to start all over.
After the glue has dried (2-3 hours, and I use Titebound white glue) I carefully cut the inlay and then file to shape. I then place the cut inlay on the stock, decide if I like the work and begin to cut it in. I have found that this method works pretty good for me, and I hope this helps for you.
Here's a sample: