Why does the Playboy appeal to you?
Ultimately, how you answer this question is up to you. What do you like about Mahon? What about him makes you identify with him? Does he make you laugh? Cry? Does he help you recognize something about yourself or others you know?
Is his willingness to accept credit for a morbid deed, then his cowardice when his father shows up, comparable to your experience in the world? Is this an accurate critique of machismo and morbidity, not only in the character of the Playboy, but also in the townspeople, as well?
Personally, I love the play much more than the character of the Playboy, himself. I see his representation as a critique of society. But that may be completely different for you.
I had a favorite class in college that included work by J.M. Synge and his relatively straightforward presentation of his characters was probably one of my favorite things about his style. The fact that the characters really seem to respond the way people I know might with all their oddities and sometimes crudities intact is in a way refreshing if you are used to more idealized characters. At the time, and as others in the post below mentioned, audiences were at certain times offended by the very realistic and somewhat explicit way that the characters responded to things. So it isn't always for everyone, but I tend to think it is a valuable part of Synge's work.
Are you referring to a character in "A Midsummer Night's Dream"? Because the only character I think comes close is Egeus-- who is more of a "reformed bachelor" than anything else.