For one thing, pannm, Disney has programmed into the reservation system that they REALLY don't like short stays of 1-2 nights.
You can get them if you book WAY in advance (the booking window opens at 499 nights before arrival).
You can get them if you book REALLY short (within a month of arrival).
In between those two timeframes, it's hard to get 1-2 nights (especially on weekends). I know from experience. And it's that way by design.
But Disney doesn't want to give a campsite to a guest who only stays 1-2 nights. They don't make as much money as one who stays 3-7 nights or longer. Short stay guests MIGHT visit one park day. But longer stay guests go to multiple parks, dine in the restaurants, buy plush generic merchandise, and spend more freely generally.
But yes, we need the specifics of what time frame they are looking for. Locals book weekends (2 nights mostly) WAY in advance so they are hard to get (until close in like 30 days before arrival if cancellations occur).
Also keep in mind that Disney has added about 20 net campsites since 1978. In that time span, the boomers have retired and gotten campers/rv's and the pandemic has caused a sales boom with people who bought campers to sleep in the own spaces and not use somebody's old hotel room.
So can you give us some specifics?
Bama Ed
PS - Disney does stupid stuff like the following: You want the nights of May 2 and 3 (in on the 2nd, out on the 4th). You enter those dates and get "No availability". You enter in May 1 and out May 8 (7 nights) instead and you get availability and sites to choose from and book. So your May 2 and 3 nights are REALLY available and Disney won't let you book them. And if you try to book May 1-May 8 and try to drop the unwanted nights, Disney has been know to say you can't do that, you have to cancel the FULL May 1-8 and try to book a new May 2-4. There is no consistency, only frustration and inconsistency from Disney. And why do they do this? Because they can.
PPS - you used the term "overnight" which to me implied a short 1-2 night stay. If they want longer, you have to book WELL in advance now. I booked January 2021 11 months in advance (4 weeknights). I booked Thanksgiving 2021 two week stay the moment the window (based on arrival day) opened 500 nights in advance.