What is a word for being obviously humorous?

Solution 1:

The word to express how humour might be delivered in a deadpan or ironic manner is:

drily (also dryly)
ADVERB

1. In a matter-of-fact or ironically humorous way.
   " 'How very observant', he said drily"
   " 'Fifty songs,' I mused. 'Five thousand dollars worth of digital matter,' I added to myself dryly."
   " 'We call it the belly of the beast,' she dryly remarks."

[Source: Oxford Living Dictionaries]

Merriam-Webster doesn't specifically define the adverb, but gives the following definition for the adjective and notes "dryly also drily adverb":

14. marked by matter-of-fact, ironic, or terse manner of expression
    a dry wit
    has a very dry sense of humor

The key in using drily is that there is an element of humour or irony inherent in the statement but the delivery itself gives no indication of humour or other emotion.