Is there a Haskell idiom for updating a nested data structure?

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Record update syntax comes standard with the compiler:

addManStk team = team {
    manager = (manager team) {
        diet = (diet (manager team)) {
             steaks = steaks (diet (manager team)) + 1
             }
        }
    }

Terrible! But there’s a better way. There are several packages on Hackage that implement functional references and lenses, which is definitely what you want to do. For example, with the fclabels package, you would put underscores in front of all your record names, then write

$(mkLabels ['BBTeam, 'Coach, 'Diet, 'BBPlayer])
addManStk = modify (+1) (steaks . diet . manager)

Edited in 2017 to add: these days there is broad consensus on the lens package being a particularly good implementation technique. While it is a very big package, there is also very good documentation and introductory material available in various places around the web.

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