Not sure how relevant this topic is due to it being posted a little over a week ago but there are a few things to add.
1) UFOs will only appear on days where there is no special town visitors (Mon-Fri) but are not necessarily guaranteed to appear. You can check with Booker at the gate to make sure just in case. If there is no special visitor that day and a UFO does not appear, Pete will be guaranteed to fly by at the 9 AM and 5 PM mark in the sky where you can choose to try to shoot him down if you want.
2) A UFO will always spawn the when the minute hand ends in a -2 or -7. (ex. 10:12 AM or 4:17 PM) And it will always appear the first -2 or -7 after first logging in (unless you exit your house on one of those minute marks, which the spawn will hop to the next available mark).
3) UFOs cannot spawn before 6 AM or after 11 PM in the weekday.
A good way to farm UFOs is to log in at the -1 or -6 minute mark when you first start playing for the day and run to the top of your town hugging on of the edges with a slingshot ready in hand. When the minute mark hits -2 or -7, run from one side to the of your town to the other (ex. left to right) and if you don't see a UFO in the sky then you will instantly know it is not going to appear that day. UFOs aren't actually all that rare, they have just as much of a chance to appear as any other town visitor- the only difficult part is knowing when it spawns and successfully shooting it down.
Most of this info is second nature to me as I learned it on my own when trying to get the Metroid item for my house in Wild World as a kid. Hope it helps and good luck!
