Maybe in your announcement (we txt ours out to friends and extended family, but call the immediate families first) say, "Baby **** is here, mum and bub are well, but exhausted. No visitors as yet, we'll let you know when we are ready" This might deter alot of the visitors... who come in for the sake of it (like just to see your DH)
Thats a great idea - will remember that one. Nice, simple, not offensive, but gets the msg across clearly.