I would approach this in the same way I approach photographing star trails, which is also my approach to photographing busy city street scenes at night. That is, you will take a series of time lapse photographs. Then in post, you will 'stack' them to add the brightest pixels of each image. You'll need a tripod, an inexpensive intervalometer, a full battery, and one of the free or inexpensive star trail software tools. I would start with exposure times of about 10 seconds, but try other times perhaps as low as 5 seconds, but perhaps as long as about 30 seconds. A series of shorter exposure photographs will give you bright fireflies with this technique. Longer exposures will reduce the average brightness of the fireflies.
Some of the star trail software packages add a few of your images to create a brightened 'foreground' image. In your case they will create the brightened backyard image. Then they will add only the bright pixels of each image. After stacking the images, you'll have a clear, fairly bright backyard and as many fireflies as were visible.
I would also shoot in RAW so you have some more control.
In regard to the intervalomter, I bought a cheap one ~ 15 USD on Amazon. It works perfectly fine.
EDIT: Based on re-reading your question, I would amend my answer to include shorter exposures if you don't want to see any motion of the fireflies. You would still apply the same technique of 'stacking' the series images you shot on your tripod.
PS. A few days ago, I traveled to a part of the country where I had a chance to try this. It worked perfectly. I tested a few different parameters. In each case I shot a series of 15 images with my cheap intervalomter. All of the variations worked as expected. I varied shutter speed from as low as 2 seconds to as high as 20 seconds. I kept ISO low, between 100 and 400. I used a gray card to ensure a had a good WB, (cameras auto WB typically aren't as accurate as it gets darker). I used a free Star trails software tool. It all worked perfectly well.
However, to me, my compositions were quite boring. I think this would be more appealing if the scene would have been appealing with out the fireflies. For example, a field of flowers.
Interestingly, in just the few minutes I tested this, I noticed the fireflies glow in waves. That is, they will all blink on for a minute or so, then they will all stay off for a couple of minutes. Then blink on for a bit, then stay off for a bit and so forth. Also, I noticed that as the evening darkened, passing cars' headlights appeared to start their glowing frenzy - but I'm not 100% sure that wasn't just a few happy coincidences.
Let us know how your shots turned out.