Andrey Serbinenko wrote:
If kept within the normal category load limits, is 172 certified to do
barrel rolls?

Andrey

No, but you can do a slip-short split-S if you so desire. I've only
done one in a low wing, but keeping positive 1g throughout is
necessary. They don't have the roll rate of an edge 540 so I don't know
why you would even want to do anything like a barrel roll in a training
aircraft. I like your live on the edge spirit though!!