As has been said in all the posts, the short answer is NO. 172 is not
certified to do barrel rolls.

However I can barrel roll a 172 only pulling 1 G which puts no more
load on airframe than straight and level flight. I have thousands of
hours to back up my statement.

No you can not.
It's not possible to even start the roll without going greater
than 1G.

Ron;
I think what might be happening here is that some folks are defining the
roll from the set point rather than from level flight. It's true that any
raising of the nose from level flight will require more than 1 g, but once
at the set point and initiating the roll (aileron roll) you can unload the
airplane all the way down to 0 g if you like right up to the backside
recovery to level flight, where the g of course has to be returned.
Dudley Henriques

Dudley, they are not paying attention. They are thinking every maneuver
has to start and be flown from the straight and level. They don't think
in terms of up/down-lines at any angle.
ie.... Reverse half-Cuban with a barrel roll on the down 45.