Unfortunately, the answer seems to be "not a lot". The government makes a lot of noise about how it is investing in Science!
So what can we do? The PCE suggests bringing nitrogen fertilisers into the ETS, since they're easily managed. This will mean higher prices, based on their decay emissions, and this should in turn discourage farmers from using them (or, in market-speak, ensure that they use them when the benefit of using them outweighs the cost). They also suggest lower stocking rates, which no government is ever going to push despite the clear benefits both for the climate and our waterways. But ultimately they suggest offsetting agricultural emissions with trees as a stopgap measure to allow us to buy more time. The scale required is enormous - a million hectares of native forest. But that's what you end up having to do when you let a polluting sector grow like a cancer for twenty years without doing anything to stop it.
The problem is that this merely pushes the problem into the future. While like John Key I hope for a scientific solution to agricultural emissions, unlike him I recognise that hope is not a strategy. Instead, its the policy equivalent of saying that you'll pay your bills by winning the lottery. Agricultural emissions are a real problem now. They are destroying the planet now. And some hoped-for magic bean future solution does absolutely nothing to solve it now. We need a solution for this in the here-and-now, not the distant future, and if the government doesn't want that solution to be shooting cows (saving ~2.5T/year per cow), they need to come up with something.