(As the subject states.)
qinggong
To be honest, Zen Archer is one of the strongest class Archetype out there in most one on one and boss fight. You wouldn't want to take any other class' archetype when you can have good saves, decent AC, good grapple in class range and one of the fastest base land speed combine with long range flurry of blow with your arrows and bow. If you are able to solve the problem of not landing enough hits, you will have very high damage.
However, if you want to have some more BAB and not giving out AoOs firing arrow when being threaten, you can take either 6 levels of ranger or 4 level of Archer(fighter's archetype) to get Point blank Mastery. Don't see it as effective if you playing a Zen archer right because you will have high wisdom and able to spot enemy respectively easy.
For flavour...anything you like. For effectiveness...ZA is pretty damn good all on its own.
here's a chart... its not infallible but its a good place to start.
on quick inspection, looks like only qinggong. (of course all that is assuming you meant other monk archetypes that stack, if you were looking for other classes with a complementary archetype i think the advice to single class is good.)