If they're all said by the same person it could be "a moanologue".
A: "What's the collective noun for a series of bad puns? I'm not sure, but 'an appreciation' is not it.."
B: "How about 'an ovation'?" 
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Seems to me it would be a groan of puns.
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Was just about to write that myself!
End of conversation
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...a punishment?
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Whatever it is, it should be a high-quality bad pun.
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