Coogan was around for a long time in show business from a kid to an old man. His signature changed significantly but I can tell you his “J” and “C” are consistent with exemplars I have seen which leads me to believe possibly “authentic”. Unfortunately, his autograph can be had for like $10, outside The Kid era.
Also, interesting that it looks like the same pen used for your Fairbanks you ripped up. Coincidence?
The pen used on this Coogan looks a lot like the pen that was used on the forged Fairbanks you showed the other day. I just wasn’t sure if it could have came from the same forger, but Coogan looks real so comment null and void.