Take a look at the CERN Neutrinos to Gran Sasso (CNGS) neutrino beam experiments. They start with a proton beam at CERN. Aim it at a carbon target. The results produces pions and kaons, which decay into muons and neutrinos. The beamline, and hence the neutrinos, was directed towards Italy.
In the experiment, they can generate pulses of 3 nanoseconds, each with up to 524 nanosecond gaps. This gives a 2MHz signal. However, not all of those pulses were detected.
If I read this right, "We report here on results based on part of the data taken during 2008 and 2009 runs, which amounted respectively to 1.78 and 3.52 × 1019 [protons on target], respectively. Among the 10122 and 21428 on-time events taken in 2008 and 2009, respectively 1698 and 3693 events were identified as candidate neutrino interactions in the target bricks."
Elsewhere, I found that the experiment ran from 27 May - 23 Nov 2009. I don't know if the beam was in continuous use for all 6 months. Let's assume it was full-time for only 1 month of that, which is unlikely.
There's a signal of some 3000 events per month, giving a transmission rate of 100 bits per day, or about 1 bit every 15 minutes. Rather a lot lower than 2MHz.
We would need some way which is about at least 1,000,000x better at detecting neutrinos before some company is willing to fund the Sydney/Wall St. neutrino beamline.
