"Every day confirms my opinion on the superiority of a vicious life - and if Virtue is not its own reward I don't know any other stipend annexed to it"

The speaker (presumably Lord Byron) is recommending that living a "vicious" or immoral life is superior to living a virtuous one. They are sarcastically acknowledging the belief that "Virtue" ought to be its own benefit, but they can not think of any other benefit associated with it. Essentially, the speaker is challenging the concept that living a virtuous life is fulfilling or important.