Assuming you've already uploaded the photos and tagged the appropriate people, here are the steps:
1. Go to the profile of the person whose profile photo you want to change
2. Click the Media tab
3. Click "View All" to the right of the "Photos of <name>" heading
4. Click on the photo that you want to be the new profile photo
5. Click the "Set Proflie Photo" button below the title (note that hovering your mouse over this button clarifies that it will set it as that person's profile photo, rather than your own -- this is because you access the photo from that person's profile)
Mike at Geni
Slightly quicker is to click their profile photo -- I should have checked our own help site first! http://help.geni.com/entries/20015877-how-can-i-change-a-profile-ph...
That's a feature request for Michelle Elena Kempner to consider. I'm not convinced it would be a clean user experience (upload a photo, then tag one or more people in it, then specify that it should be the profile photo for one or more of the tagged people?) but that's why I'm an engineer and not a product person.