ablogogize 

To apologize someone via blog. Other forms, "ablogogy."

Jack was a dick to me at the party last night, if I didn't see his attempt to ablogogize on myspace this morning I would still be pissed at him.

ablogogize by LovedByMagmo January 11, 2009

aLOLogize 

–verb (used without object), -gized, -giz·ing.
1.
to offer a compassionate laugh, as for suffering or trouble

2.
to express sympathy or console by use of humor.

Gary aLOLogized with Denise after the death of her favorite stuffed dog.

aLOLogize by Nivush November 3, 2010

Aplologize 

To laugh out loud while making an apology.

Person 1: "Ow, what the hell, you hit me in the eye!
Person 2: "Hahaha! Haha, sorry, haha!

Fred aplologized to Mark.

Aplologize by PaperStrike May 13, 2009