Manufacturing serendipity is a tricky business, as the makers of any number of whimsical, failed television series can tell you. Jemaine Clement and Bret McKenzie managed it better than most in the first 12-episode season of “Flight of the Conchords” on HBO last year. Season 2 begins on Sunday (the first episode is already available at hbo.com), and the off-kilter charm is still there, though some strain is beginning to show.

This fish-out-of-water sitcom about a pair of guileless New Zealand musicians bumbling through life in New York has a formula and sticks to it: stretches of surrealist, deadpan comedy, so minimal as to be barely there, alternate with comparatively elaborate, Michel Gondry-style fantastical musical numbers.

The “Seinfeld”-like plots are spun from air: Bret buys a mug for $2.79 and plunges the duo into such dire economic straits that Jemaine takes up prostitution, complete with a “Midnight Cowboy” hotel room parody. (“I have a few rules. One, no laughing, especially during, O.K.? Put’s me off.”) During a performance in a library, Bret ad-libs insults to some prominent rappers, then forms his own gang  which includes the middle-aged Asian proprietors of the Internet cafe downstairs  in case Snoop Dogg or Missy Elliott comes looking for him.