I got pretty lucky. In September, about 2 months of playing the game, I was remodeling my town. Wendy, one of my default villagers, pinged me and suggested it c:
I've waited for about 3 months before actually having it requested. I'm not sure why it takes forever for it to be requested. I wish it was something you could install from the very beginning.
I restarted my town in May 7th, and it took until 1 month to get it, can't remember the date I got it but I did. I chose the Wooden Style as my police station and placed it in that big empty spot I had on the southeast side of the town hall. Now I have paths that shaped like a planned villager house plot at the right side of the police station whenever I get Diana. And when I do, i'm going to try out that "TTing backwards with the plot gone but still get it by TT to the normal time" Uffe told me about.
Ugh I've been trying to ping for the Police Station for so long.. My GF starts a new town last week and gets the Police Station along with 4 more PWPs in a week..
Gladys was awesome enough to request in Celadon after a few months of having the game. I haven't built it, though. It hasn't been requested at all in Chrome or Trout.
It took me six months to get mine. I wasn't even aware it was possible to unlock it until I was four months in, and then I anxiously waited for it for another two.
I just got police station request in my second town C: I started my new town only a few days ago but I've been TTing day by day so it's been like a month in the game.. It was actually first PWP request I got from a villager! I got so lucky there C:
My first, main town took months like others.. Anyways, congrats C: