My wife always jokes that a Yom Kippur bris is the best. You know that
everyone has to be there, and you don't have to feed them anything.
btw, there is one rule regarding having a bris on Shabbos or Yom Tov. If
the baby is born Bein Hashmashot (twilight, between sundown and nightfall),
the bris gets pushed forward. The reasoning is as follows:
Bein Hashmashot is considered a Safek (in question) as to whether it
belongs to the previous day or the night of the next day. As such we
always error on the side of caution (this is why we start Shabbos at
sundown, but don't end it until nightfall). If the baby were born during
this period, we are not positive if the baby was born on Fri. or Shabbos.
We couldn't have the bris on the following Fri. because if it was really
Shabbos, we aren't having the bris on the eight day. We couldn't have the
bris on Shabbos, because we are only allowed to violate Shabbos if it is
necessary, if the baby were really born on Fri. it would be the ninth day,
and we couldn't violate the Shabbos for a bris on the ninth day. In such a
case the bris would be on Sunday. The same would hold true for a Yom Tov.
(this happened with my nephew on a Shabbos)