Jokes/tale to song - oldies. ZN numbers locate the songs in the broadside ballad index on my website.

A. C. Mery Talys, 1526 = ACMT
Rowland's Godson (mistress and apprentice convince foolish husband he didn't see them in bed) ACMT #3 and Heptameron; ZN2546
Of the maid washing clothes and answered the friar, ACMT #23; "Stow the Friar" in Pills to Purge Melancholy
Of the gentleman that base the siege board around his neck, ACMT #26; tale and song recent "Bonnie Wee Window" thread and DT's WEEWINDO
Cuckold Cap, ACMT #28; song version in The Merry Medley, and broadside in Holloway and Black's 'Later English Broadside Ballads', I, #78
The dumb maid, ACMT #62; ZN143, DT file DUMBDUMB
Butcher and the Taylors wife, ACMT #76 & Les Cent Nouvelles, Nouvelles, #4
Man with two sons, ACMT #96; miller's will adds another son
Burning of old John, ACMT #100, broadside on my website.

From Tales and Quick Answers, c 1535, T&QA, the following twist on the Widow of Westmorland's daughter"

There was a man upon a time which proffered his daughter to a young man in marriage, the which the young man refused her, saying that she was too young to be married.
"I wis," quoth her foolish father, "she is more able than ye ween. For she hath borne three children by our parish clerk"

There's a variant where the smarter father admitted his daughter had borne a child, "But it was only a very little one". An analogue in later jokes is that the daughter is 'slightly pregnant' [more direct Widow's Daughter below]

Of the merchant that lost his budget between Ware and London, T&QA #16; [Solomon and his jester Marcolf] Percy Folio MS and broadside, ZN1528
Of the jealous man T&QA [Carvel's Ring] song versions with tunes on my website
Of him that sought his wife against the stream, T&QA, #55, song in Merry Medley, 1744 [Tale from 1001 nights]
Of the young man of Bruges and his spouse, T&QA #73, and Les Cent Nouelles Nouvelles; "Widow of Westmorland's daughter".

There are some good jokes that would make good songs, but for which I've found no song version, e.g.,

Wits, Fits and Fancies, 1614:

A man had a shrewd wife, and one day broke her head, the cure wherof cost him dear expense afterwards; insomuch that his wife in regard thereof said on a time unto her Gossips, "Faith, my husband will not dare give me no more broken heads in haste, considering how dear he finds them in the cure."
Her husband, hearing of such her braves [boasts] sent the next day for the Surgeons and Apothecaries, and in her presence paid them all their bills and gave each of them twenty shillings over and above, saying, "Hold this, Sirs, against the next time."

Legman, in 'The Hornbook', gives the modern erotic version:

A Jewish rabbi temporarily replaces a Catholic priest in the confessional, and deals out identical penances to the women who present themselves for absolution; telling the last woman (who had sinned only once) to say their paternosters and put three dollars in the poor-box and the church will owe her two more acts of intercourse.
This stumped Legman, who couldn't figure out if it was anti- Jewish, or anti-Catholic.

Errant friars and women's (including nuns) confessions are common in old stories [Decameron, Heptameron, Tales of Alfonse and Poge, Les Cent Nouvelles] too many to keep track of. See the bawdy Fryar and the Nun on my website for such an English song, and its remarkable reoccurrence in a book of Christmas carols.

Here's one of c 1710 that's been widely reprinted, but seems to have escaped the DT so far. This was also called "The Friar and the Nun" which occasionally leads to confusion about its tune, which appears under both titles in the Irish tune index on my website, but isn't the old tune called "The Friar and the Nun"

A Lovely Lass to a friar came
To confess in the morning early,
In what, my dear, are you to blame?
Come tell me most sincerely."
"I have done, sir, what I dare not name,
With a lad that loves me dearly.

"The greatest fault in myself I know
In what I now discover."
"You for that fault to Rome must go
Or discipline would suffer."
"Lack-a-day, sir, if it must be so,
Pray send me with my lover."

"Oh, no, no, no, my dear, you dream;
We'll have no double-dealing.
But if with me you'll repeat the same
I'll pardon your past failing."
"I own, sir, but I blush with shame,
Your penance is prevailing."

[ABC of tune for this is B296 on my website]

There's another song I can't find at the moment: Nun Jane had confessed that she had slept with a man and got a very light penance. Two other nuns, knowing they would get a penance no matter what they did, decided to follow Jane's example.

But it didn't do to over-do that sort of thing, as two nuns discovered in another tale. The fair young nun who slept with a young man only once got a light penance, but the older nun who slept with an old friar twice, only God could forgive, the confessor couldn't.

Unfortunately, we do not have the song of tune of another piece of 1614:
A gentleman that played very well on the Bandore [roughly bass guitar] and had but a bad voice played and sung in an Evening under his Mistress's window, and when he had done, asked her how she liked his music. She answered, "You have played very well, and you have sung too." [Politically Correct is nothing new]

There's a common tale, in Gargantua and Pantagruel, one of Andrew Borde's joke books (last two by Drs. that had been friars), and later, 1583, in the Mirror of Fancies. It's the one of the friar that always answered all questions in a single word of one syllable. That's not easy to put in a song.

The "Song of the Cobbler of Romney" in 'The Tinker of Turvy' (mostly drawn from cuckolding tales of the Decameron, 1630, is taken from Les Cent Nouvelles Nouvelles. [Friars often played a role in cuckolding tales.]

"The Crossed Couple", c 1660, which is on my website (with tune and notes of some more song versions) and a tale version in Randolph's 'Pissing in the Snow' appears as a tale in Les Cent Nouvelles Nouvelles.
"The Lusty Friar of Flanders" and "The Cowardly Clown of Flanders Cuckolded" in my broadside index are probably both from tale versions, but I have looked for them. Also, there are now less than 3 versions (cross-referenced) of "A Cuckold by Consent", on my website, that undoubtedly springs from a tale ["There was an X, he had a fair wife, the Y he loved her, as dearly as his life" is a common beginning for a song of a cuckolding.]

Maybe some more if I get ambitious.