Are there ages where appendicitis is a more common cause of stomach pain?

No. Appendicitis can occur at any age. Cases have even been reported in infants.
Yes. Appendicitis ocurrs quite frequently in the first two decades of life. The younger are less able to convey to their parents how they feel and thus the perforation rate is higher in those under 5 years. Pain in the right lower quadrant in a child who does not want to walk should make a parent suspicious and seek medical attention.
Yes. Appendicitis is most common in teenagers; 2/3 of all cases in the US occur prior to age 30. Nevertheless, I have operated on 3-yr olds and 90-yr olds for appendicitis. Overall, people in the US have a lifetime risk of about 1:12 of having appendicitis.