Go out in the driveway, run the motor for a while, and prepare the Jiffy Pop on your engine block.
I have made it on my newish glass stovetop many times without any problems. I even let my kids do it without worry. I didn’t even know about the warning because I have been making it since I was little and didn’t reread the directions.
I bought jiffy pop for my daughters. The disposable, no mess solution was a hit with our family.
Popcorn is reasonably good.
Microwave popcorn has too many chemicals in it. Even the butter taste comes from a lab.
Another vote that it’s just a CYA label. We do Jiffy Pop from time to time on our glass top stove without clouds of poison gas being released.
Okay, on these recommendations, I’ll stop agitating the pot. But if my popcorn starts to burn, I’m sending the Straight Dope a bill for each kernel! 
Sorry, but I don’t believe the aluminum foil that Jiffy Pop pans are made of is even hard enough to scratch a glass cooktop. In fact, back in my college days, we sometimes used aluminum foil as a scrubber for cleaning Pyrex lab wear and it never scratched the glass. Maybe some exotic aluminum alloys could do it, but not some cheap throw away like a Jiffy Pop pan.
I’ve had a glass top stove for years and wouldn’t hesitate for a second to use it for Jiffy Pop.
I just made some popcorn. In duckfat (yum). A few kernels burned. I didn’t eat them. Popcorn is cheap, and losing a tiny fraction of kernels is less costly than standing there shaking my frying pan for the entire cook.
I thought that JiffyPop went out of business years ago. IIRC, they blamed it on trans fats, but they’d been going steadily downhill for a long time.
[ side question] Did you just make this up? Wow does it sound American classic, but I’ve never read it/heard it.
[/side question]
Yes, or a regular pan large enough to let you shake the Jiffy Pop. An added benefit is that the pan would even out the temperature should the stove turn the heat on and off.
As implied by the duckfat poster above, the slick of any kind oil in a pan adds a flicker or taste to each; butter is out, because it will burn before it can do the job of popping the darn things. In addition–and I have no idea how this affects taste, time, etc., but I’m sure the ConAgra people do–the oil coating of each kernel is a far more efficient transmitter of heat than air. In pan-size preparations, as opposed to movie-theater-and-up batches.
[side answer]Well I’ll be dipped in shit. You Vermont folk.[/side answer]
Indeed. You need enough oil to properly transmit heat or the popcorn will burn without popping.
Olive oil is fussy because it has a low smoke point, but it’s yummy. Duck fat and goose fat are nearly perfect for popping corn. Ghee is also tasty. Peanut oil is neutral (rather than yummy) but has a high smoke point so it’s easy to use.
Clarified butter will work. It’s the solids in butter that burn at relatively low temperatures. Clarified butter has a pretty high smoke point (485 F/252C), which should be high enough for making popcorn.
As for peanut oil, the brands you get in a grocery store are usually purified to the point of having no flavor. Imported peanut oils carried in Asian grocery stores can have a lot of flavor. Lion Globe is a good brand.
Sesame oil is another good one for flavor, especially if you use toasted black sesame oil. The flavor is pretty strong, though, so you may want to mix it with a neutrally flavored oil such as canola oil.
Since we’re on the subject, coconut oil is the only oil to use for popping corn. There’s nothing else even close.
Only if it’s extra virgin, and you should be using that raw anyway to get the most out of its flavor. Refined olive oil has a smoke point as high as any other you’d care to use.
Stoves with glass or ceramic tops use induction coils to produce heat. That’s how it transfers heat to a metal pan but won’t burn your bare hand. The Jiffy Pop people are probably concerned that the induction won’t work right because the aluminum foil “pan” is too thin.
Actually a variant on this might be your solution.
Buy a disposable aluminum pie pan. (Actually, they’re sold in packs, so you’ll have several.)
Take a pie pan, cut the bottom out of it.
Place the pan on your burner. You may have to experiment a bit to see which end up works the best. You might have to trim it down a bit to get the bottom of the JiffyPop pan the right distance from the burner.
Place the JiffyPop pan on top of the disposable pan.
Pop.
If you happen to have a wok ring from back in the day when we all had woks, you could try that too.
Hope this helps.
Also you might try using a rangetop liner for gas stoves, lay that over the burner …
Actually, they sell 'em for induction cooktops!
Eh, extra virgin olive oil tastes good when cooked. The popcorn is very nice, although ghee and goose fat are my favorites.