You should check the park guide for daily appearances of characters.
Here's what this past weeks park guide said - these are pretty regular shows:
Toon Lagoon Bash - hang ten with your favorite cartoon and comic strip superstars. They're dancing in the street and want you to join the fun - 11:30am, 12:30pm, 2:30pm, 3:30pm, 4:30pm and 5:30pm (I know for a fact you will see popeye at this one and the chracter come into the crowd afterwards and hug the kids and sign autograpgs)
Confisco Character Cafe - Enjoy lunch at Confisco grille while a cast of Islands of Adventure characaters visit your table. Meet, greet and eat with all of your favorites! 12 Noon - 2pm Daily (again, have seen popeye here)
Also, have seen Popey et. al. do meet and greats in Toon Lagoon at various times throughout the day.
Kidzone Trolley Character Meet and Great - Swing by the entrance to E.T. Adventure for pictures and autographs as a trolley full of your favorite cartoon stars pulls in for it's next scheduled stop! 11:15am, 12:30pm, 1:45pm, 3:30pm, 4:45pm (sorry I have no first hand experience of this one so I can't tell you if the rugrats appear)
I also think I have seen the rugrats doing autograph sessions near Nikleodean, but I cannot be 100% possitive, sorry.
Hope this helps.