A custom Map is easy made by using the Website: 

Snazzy Maps - Free Styles for Google Maps

There you can explore different map styles and choos one of your likings.

Click on the design you like or create you own.

If you have chosen one you can insert you adress or hometown on the right side of the screen. Adjust the wanted area and export with 3x to have better quality. (You need to register to export or take screenshot if that quality is enough for you)

1. Insert coaster into the M1 and refresh to get a rough estimate of the size.
2. Create a circle thats fitting the coaster
3. Import Map Image
4. Use adjustment Panel and turn up Sharpness to 80
5. Select circle and image and click on the right panel to turn it into a mask to only have the map inside the circle

I just went with the above settings by guess and worked out fine for me

I'm really in love with the results of the engraving. This was way better than I could imagine it. If you don't know the area you wouldn't get it but its recognisable.

I hope the page to create own maps easily helps. Have fun creating! ~Anzy