There aren't that many 'comedy' songs in the tradition, but there are a great number of humourous ones - the former rely on a punch line, and have little else, but the genuinely humourous ones are based on cleverness and trickery, and quite often have wider implications - a servant getting the better of his master, a 'weaker' woman, outwitting a dominant man, a city slicker being floored by a local 'bumkin'
Probably, the most dominant and entertaining of the humourous songs are the ballads - 'King John and the Bishop', 'The Duke of Atholl's Nurse', 'Long Johnny Moore'.
Probably the longest surviving of these, 'Get up and Bar the Door', appears in song and story and dates back to Ancient Egypt, and was still to be found among Irish Travellers in thwe 1970s as a cante-fable

12 - Go for the Water (Story - Aarne-Thompson 1351:The Silence Wager)   
Mikeen McCarthy, Cahersiveen, Kerry
There was a brother and sister one time, they were back in the West of Kerry altogether, oh, and a very remote place altogether now. So the water was that far away from them that they used always be grumbling and grousing, the two of them, now, which of them’d go for the water. So they’d always come to the decision anyway, that they’d have their little couple of verses and who’d ever stop first, they’d have to go for the water. So, they’d sit at both sides of the fire, anyway, and there was two little hobs that time, there used be no chairs, only two hobs, and one’d be sitting at one side and the other at the other side and maybe Jack’d have a wee dúidín (doodeen), d’you know, that’s what they used call a little clay pipe (te). And Jack’d say:
(Sung)
Oren hum dum di deedle o de doo rum day,
Racks fol de voedleen the vo vo vee.

So now it would go over to Mary:
Oren him iren ooren hun the roo ry ray,
Racks fol de voedleen the vo vo vee.

So back to Jack again:
Oren him iren ooren hum the roo ry ray,
Rack fol de voedleen the vo vo vee.

So, they’d keep on like that maybe, from the start, from morning, maybe until night, and who’d ever stop he’d have to go for the water.
So, there was an old man from Tralee, anyway, and he was driving a horse and sidecar, ‘twas… they’d be calling it a taxi now. He’d come on with his horse and sidecar, maybe from a railway station or someplace and they’d hire him to drive him back to the west of Dingle. So, bejay, he lost his way, anyway. So ‘twas the only house now for another four or five miles. So in he goes anyway, to enquire what road he’d to take, anyway, and when he landed inside the door, he said: "How do I get to Ballyferriter from here?" And Mary said:

(Sung verse)

So over he went, he said, "What’s wrong with that one, she must be mad or something", and over to the old man. He said, "How do I get to Ballyferriter from here?"

(Sung verse)

So he just finished a verse and he go back over to Mary and he was getting the same results off of Mary; back to Jack. So the old man, he couldn’t take a chance to go off without getting the information where the place was, so he catches a hold of Mary and started tearing Mary round the place. "Show me the road to Ballyferriter", he go, and he shaking and pushing her and pull her and everything:

(Sung verse)

And he kept pulling her and pulling her and tearing her anyway, round the place, and he kept pucking her and everything.
"Oh, Jack," says she, "will you save me?"
"Oh, I will, Mary," he said, "but you’ll have to go for the water now."

Mikeen’s story, set in his own native Kerry, is widely travelled, both as a tale and as a ballad. A version from India, entitled The Farmer, his Wife and the Open Door is described as claiming ‘the highest possible antiquity’. It is also included, as part of a longer story, in Straparola’s Most Delectable Nights (Venice 1553). In Britain it is popular in ballad form, best known in Scotland as Get Up and Bar the Door and in England as John Blunt.
Mikeen has a large repertoire of stories, at least half a dozen of them having Jack and Mary as hero and heroine.
Ref: Folk Tales of All Nations, F H Lee, George G Harrap & Co, 1931.

For me, these 'humourous' songs never lose their edge, while the 'joke' ones pale after a few hearings
In my opinion, the genuinely 'comic' song possibly originate from outside the traditional communities and have little more significance than producing a quick 'laugh'
Quite often the teller feels the need to 'act them out' with gestures and funny-faces
Jim Carroll