One case could be in 2 Corinthians 12:13. Paul is writing to the Corinthians and mentions that he hasn't been a burden to them, presumably financially, but has labored among them nonetheless.
For in what were you less favored than the rest of the churches,
except that I myself did not burden you? Forgive me this wrong! 2 Corinthians 12:13 ESV
The "Forgive me this wrong" definitely seems a bit sarcastic. "Forgive me for not being a burden to you."
Another one isn't really sarcasm, but it does strike me as a bit humorous. It's from the gospel of John, which is held to have been written by John, and He seems to refer to Himself as "the other disciple".
3 So Peter and the other disciple started for the tomb. 4 Both were
running, but the other disciple outran Peter and reached the tomb
first. 5 He bent over and looked in at the strips of linen lying there
but did not go in. 6 Then Simon Peter, who was behind him, arrived and
went into the tomb. He saw the strips of linen lying there, 7 as well
as the burial cloth that had been around Jesus’ head. The cloth was
folded up by itself, separate from the linen. 8 Finally the other
disciple, who had reached the tomb first, also went inside. He saw and
believed. John 20:3-8 NIV
John seems to make sure we understand that he won the race to the tomb! :)