you could tell them that the date has changed to a couple of days later due to a double booking with the dr or something, then just call them when you are feeling up to having visitors.
when i had DS on a saturday, by the monday i was so fed up of having visitors, people were turning up at non-visiting times even tho we had told everyone what time it was, so i was trying to bf with the lactation consultant, i'm sitting there with my top off and in walks DH's family like they own the joint. or i was having a nap during the hospitals rest time (1.30 to 3.30 all the lights go off and all the nurses don't make any noise whatsoever so we could all have a good rest). also i was stuck in bed with the IV attached to me and there were about 6 people in the room all talking really loud and DH was trying to change DS's first pooey nappy and didn't know how to do it, so i was trying to talk over the top of everyone, i got so annoyed i told DH i didn't want any visitors at all the next day.
so no i don't think it is unreasonable to not want visitors the first day. actually i had never thought of that, i might just do the same and tell everyone the wrong date from the get go!
good luck i hope you get it sorted out with everyone.