How do you say "puppy eyes" in Martian? That's easy! It's "J'onn J'onzz"!
The Martian Manhunter took a complete turnaround when he got revamped with DC's New 52. He no longer was part of the original Justice League and he got stripped out of all the softness that grew around him in the 80's, 90's and the first decade of the millennium, and he got turned into a two-dimensional Wildstorm fighting machine as part of the new Stormwatch.
As many characters that got reinvented with the relaunch, he slowly started to get back to his senses… well, at least back to who he used to be. He joined the new Justice League of America for the first time in this continuity and from there he started to mellow down until he reached a new level of cuteness and mellowness, as seen in the latest issue of this JL book (that would be Justice League of America #9, 2013).
Once again he cared for his teammates as if he knew them for his entire life, showing a sense of humanity that many human beings lack. All of a sudden, I saw him like the father figure he used to be at the Bwah-haha League as he interacted with Stargirl.
Yes, the Martian Manhunter seems to have come back.