I still have a few of those old house phones from a bygone era in the house with caller ID. The caller ID display is usually powered by some AA/AAA batteries that seem like they always need to be replaced that of course no one gets around to replacing. I decided to fix this annoying issue once and for all!
The solution: A 7805 regulator with a barrel jack crammed into the phone base to plug in a wall-wart.
I started out with a phone that was destined for the bin, so if it went horribly wrong it would be no big deal. Inside, there appeared to be enough room to cram in a 7805 regulator and a barrel jack. Since the caller ID doesn't draw much power, there's no concern of the 7805 getting hot. The cheap linear regulator should do just fine. The phone used 4 AA batteries (6 volts), but I thought it would likely still work fine with only 5 volts from the 7805 (although I probably should have tested it beforehand to confirm.)
My first task was to find a suitable location to cut out a hole for the barrel jack. I decided to use the open space in the back. It wasn't feasible to get a drill bit in there to make a nice clean hole, so I used a Dremel with a ball mill bit. The hole is a bit less than perfect but it's not of much concern as it would be hidden from plain sight.
I then soldered a 7805 do a power supply board (forgot to make the cap footprints 0805 sized, but it appears that 0805 caps will just barely fit.)
As for wiring I could have simply have just hooked up everything strait up to the leads connected to the caller ID circuitry, but for some strange reason I wanted the preserve the ability to use batteries so I cut the lead between the ground battery terminal and caller ID circuitry and connected the ground battery terminal segment to the insertion detection pin of the barrel jack and the caller ID circuitry end to the ground on the 7805 PCB. I then ran a wire from the 5V output of the 7805 and soldered it to the positive battery terminal. When nothing is plugged into the barrel jack the insertion detected pin and sleeve pins are shorted together allowing a battery to power the caller ID. I've included a very crude, cringe-worthy schematic to help explain things better.
I then soldered everything together and hot-glued it in place.
I put everything back together and it worked just fine. Problem solved.