I made a few calculations, and came up with I belive ideal coordinates (center) for large maps (256 x 256).
Result is not 'symetrical' (impossible to achieve) but it's the best compromise between harmonious and complete coverage of the map.

- Fire: 19, 56, 92, 128, 164, 201, 238 (optimal radius is 26, which gives about 37 between each station; funding 110%)
- Police: 23, 65, 107, 150, 192, 234 (optimal radius is 30, which gives about 42 between each station, funding ~108%)

Attached, you'll find tables with all coordinates.
You can display coordinates in-game by pressing SHIFT+C. When you build, since mouse cursor gives top left building coordinates, you can substract 1 to all (center) coordinates (stations are 3 x 3).

Sources: game and this website.

So you just manually calculated this instead of just looking at the map provided ingame?

Yes, but I tested these values of course! The numbers should be fine!

Edit: actually made a few mistakes with the values and forgot a Fire Station (there are 7 while only 6 Police Stations). Tables updated and now correct hopefully!.

Added pictures for you to see the result!