Typically you see references to percent of population under 18 or under 25. However are the young children really in the streets?
My guess is that protesters are in the 15-24 range.
Countries that have the highest population growth rates actually don't have the highest percent of people in that age range, as the 0-14 aged children account for a large percent.
What probably matters is youth population (15-24) as a percent of the total population that is 15 or older. Unless young children act as a "drag" on revolution (perhaps as their older siblings need to care for them or work to earn money for them). My guess is that older adults put more of a drag on revolution than young children.
It is countries that had a baby boom 20 years ago, like Iran, that have the highest percent of youth (aged 15-24). Was Khamenei encouraging a baby boom to fight the war against Iraq? My data is from 2006, so 20 years ago would be in the middle of the Iran/Iraq war. Iran's percent of 15-24 youth, at 25.2% is an outlier. It is 3% more than second place: Yemen.
Rich gulf countries (UAE, Kuwait, Bahrain, Qatar) that import workers have a lot of people in the 20-45 range, as they've imported people who don't bring their children. For instance, Qatar has four times more people age 25-29 than 15-19 (or 10-14)! Most of these foreign workers are men (perhaps 90%).
Outside of Iran and the Rich Gulf States, the remaining countries have roughly the same percent of youth. Between Yemen and Tunisia there is only a range of 10%. Youth might be revolting, but I suspect every country has enough young people to do a revolt given favorable conditions. There were probably much smaller youth populations in Eastern Europe and the former-USSR when those dictatorships fell.
Source: 2006-2008 UN data. I forgot the link. I calculated the percent myself by adding the 15-19 and 20-24 age groups, and dividing by the total population.