I wish someone more expert could help you here!
(I'm NOT an expert at this!!)
What I'd do is not tamper with the pattern, but either use a part of it that would fit the coaster.
Or else use a smaller count aida - that is there are more squares of aida per inch in the aida you'd use for the coaster, so maybe by using 18 or 24 count aida you can have a smaller version of your pattern that can fit the coaster.
Hope this helps you a bit. Or maybe someone with better knowledge can jump in soon and help!!