I think it is hard to come up with any credible argument that would suggest this excellent play is a tragedy. The light-hearted, flippant tone of the play combined with the way that it pokes fun at the norms and values of the day clearly points towards its status as a comedy. You might want to consider how such issues such as marriage are presented in the play in a completely irreverent fashion. Consider the following quote from the beginning of the play, when Algernon talks to Jack about proposing:
I really don't see anything romantic in proposing. It is very romantic to be in love. But there is nothing romantic about a definite proposal. Why, one may be accepted. One usually is, I believe. Then the excitement is all over. The very essence of romance is uncertainty. If ever I get married, I'll certainly try to forget the fact.
The way in which Algernon confidently asserts that he will do his best to forget being married when he is married obviously suggests the humour and flippancy of what he is half-seriously saying. There is no sense that this play could be regarded as a tragedy when it goes to such lengths to expose the hypocrisy of Victorian society and to highlight its various absurdities.