When it comes to changing diapers, Donte Palmer has his technique down.

After all, when public restrooms do not offer a place to change his son’s diaper, Mr. Palmer has to get creative: He squats low, against a wall, and lays Liam across his lap. His 12-year-old son, Isaiah Wells-Thomas, gives him a hand, disposing of wipes and soiled diapers.

Last month, when Mr. Palmer was going through the motions of squatting in a bathroom stall at a restaurant in Jacksonville, Fla., Isaiah took out his phone and snapped a photo.

Mr. Palmer, a high school teacher in Jacksonville, decided to post it online to show how routine the maneuver had become for his son, thinking he would get some reaction from friends. But a popular Instagram account reposted his photo, and soon, local and national media outlets picked up his story.

Messages of support from around the world — from fathers as far away as Australia, Japan and Uganda — flooded in.