For me, "scone-athon" rhymes, but perhaps for you it would need to be a "scone-athone".
Both pronunciations, one rhyming with "con" and the other with "cone" coexist on both sides of the Atlantic.
In the US "cone" is more common.
The Canadian Oxford Dictionary lists "con" first, which suggests that our pronunciation survey revealed that that pronunciation was more common in Canada. It could have been a 55%-45% split, I don't actually remember, and my general feeling is that "cone" may in fact be more common in Canada, so please let me know which one you use.
The Oxford Dictionary of English has this intriguing comment about British English usage:
In British English the two pronunciations traditionally have different regional and class associations, with the first pronunciation (CON) associated with the north of England and the northern working class, while the second (CONE) is associated with the south and the middle class.
Here's a map based on a survey the Daily Telegraph did in 2016:
The Oxford Dictionary of English continues:
In modern British English, however, it has become fashionable among certain middle-class people to adopt the first pronunciation.
I find this interesting because I first encountered scones as a child in southern England in a middle class -- and resolutely unfashionable -- family (a Canadian one, though). I have always rhymed scone with con.
The word was originally Scottish, and definitely pronounced "scon", judging from the spellings from the 15th to 18th century. If the "con" pronunciation is indeed more common in Canada, we probably owe it to the heavy Scottish influence on Canadian English. The word is perhaps a shortened adoption of Middle Dutch schoonbrot, Middle Low German schonbrot ‘fine bread’.
In Australia and New Zealand, they apparently love their scones (rhyming only with cons) so much (and indeed I had a mighty fine tea at the Queen Victoria Tea Rooms in Sydney) that they use "scone" as a slang synonym for "head" and have developed some delightful idiomatic expressions:
do one's scone (Aust. & NZ colloq.) become angry.
scone-hot (NZ colloq.) excellent
go a person scone-hot (Aust. colloq. dated) attack a person with vigour, especially verbally; become angry with him or her (she went him scone-hot for not paying the light bill in time).
off one's scone (Aust. colloq.) crazy; insane.
"scone n." The Australian Oxford Dictionary, 2nd edition. Ed. Bruce Moore. Oxford University Press, 2004. Oxford Reference Online. Oxford University Press.
If all this is making you salivate, here's the Word Lady's famous scone recipe, much lauded by her friends (because in addition to being a word lover and ballet lover, Word Lady is quite the baker). You can literally "do your scone" (but not in the Antipodean sense). Yum! Enjoy your tea!
2 c. white flour
1 c. whole wheat flour
2 1/2 tsp. baking powder
1/2 tsp. baking soda
3/4 c. sugar
grated rind of one orange
Using a pastry blender or two knives, cut in
3/4 c. butter
until the butter is in small pieces.
3/4 c. raisins
1 c. buttermilk or plain yogourt
Combine with a wooden spoon until all wet ingredients are just incorporated into dry. Turn out onto a lightly floured board. Knead lightly a few times then pat to 3/4" thick. Cut out 2-inch rounds (I use a wine glass), place on ungreased cookie sheet and bake at 375 degrees for 15-17 minutes or until lightly browned.