I heard a tip about phone book advertisements/yellow pages etc -

since it alphabetical listed start with A, AA or AAA to be listed in the first batch - websites might come up the same way...not sure

AAA+ family support services?
or any variation of that or the others suggested previously

If you make your own site ?
when you try the names it will let you know if it is taken already, then you can add or change something to try it again.