Practice slowly and build up your speed:
Ten Arpeggio Exercises Plus a Song to Improve Your Fingerpicking on Ukulele
Ukulele Tabs, Tips, Chords and News Online. The Number One Ukulele Website.
And some more fingerpicking patterns and tunes:
Fingerpicking Ukulele Lessons
Ukulele Tabs, Tips, Chords and News Online. The Number One Ukulele Website.