The question becomes: is there a need for a stretch buttonhole? If you look a ready-to-wear t-shirts with functioning buttonholes (they're rare, but they do exist) you will see that the buttonholes look just like regular ones. So yesterday, after shortening a t-shirt dress that was too short to be a dress and too long to be tucked into my jeans, I used the extra to try some buttonholes.
I had seen on PeacockChic that kitchen paper makes good stabiliser for buttonholes on stretch fabric. I didn't have any kitchen paper handy so I used tissue instead.
The first buttonhole was without stabiliser, and with a ballpoint needle, you know, the ones that are supposed to prevent skipped stitches. As you can see, that was a waste of time.
Next I tried with a universal needle and tissue as stabiliser.
In fairness, I had stretched this buttonhole to see the result. This is why you need a gimp thread (for which I used topstitching thread). Take two:
That's much better. If I had been making a garment, I would have used matching-coloured gimp thread and taken the ends through to the inside of the facing, but for practice there wasn't much point.
Now of course, if you have a tug-of-war with it, it will stretch (what wouldn't?) but for real-life use I think this is perfectly fine.
So you don't need a stretch buttonhole on your sewing machine, even for jersey. (I have one, but I like this buttonhole, don't you?)