Back when I was a physics student, I helped engineer exactly this experiment as a off-the-shelf solution for schools as a classroom experiment! We used PMTs mounted on top of coffee cans:
The FTL muons produce Cherenkov radiation in the water in the coffee cans, which is picked up by the PMTs.
Using this setup gives a much higher rate, as the surface is much larger compared to geiger tubes. Thus it's possible to quickly capture a sufficient amount of muons.
http://kamiokanne.uni-goettingen.de/gb/kamiokanne.htm
The FTL muons produce Cherenkov radiation in the water in the coffee cans, which is picked up by the PMTs.
Using this setup gives a much higher rate, as the surface is much larger compared to geiger tubes. Thus it's possible to quickly capture a sufficient amount of muons.