You can get Uxie in Nameless Cavern (A Mirage Stop near Sootoplis City) from the times 20:00/ 8:00 PM and 21:00/9:00 PM.
Hope this helps!
You need to have 3 Pokemon with maximum Happiness. You need to soar using the Eon Flute with [email protected] to find the Nameless Cavern. Go there between 8:00pm - 8:59pm to encounter Uxie.