For those of you not familiar with the New Zealand scene, it was proposed that farmers be charged for the methane that their animals, and especially their ruminant animals produce. This was quickly branded the fart tax which may have contributed to the idea being shelved. The whole idea was based on faulty science.
The carbon in the flatulence produced by cows and sheep is carbon which has recently being removed from the atmosphere by the grass that the cows eat. It is a cycle. Moreover, not all the carbon is returned to the atmosphere. Some of it is sequestered, at least for a while, by people who eat beef and mutton. If anything, the farmers should be given a small carbon credit for their efforts.
The only slight justification for the tax is that methane is a stronger greenhouse gas than carbon dioxide. However, methane is fairly rapidly oxidized in the atmosphere and in the soil resulting in Carbon dioxide so this is a pretty weak argument.
One might make a case for charging farmers for the diesel they burn (as long as it is from mineral oil and not from the local fish and chip shop) as this represents a release of geologically sequestered carbon into the atmosphere. If so, the same would apply to anyone who drives a vehicle. Trying to tax the whole population should effectively knock the whole plan on the head.