There is so much evidens, that it is possible to grow rice with ten-fold reduced methane emissions, but getting the message thru seems harder. These are the links I found on the first half of the first page in a search (DuckDuckGo).
The solutions range from very basic farming methods, over using natural bacteria, to genetically modified crops. The obvious would be to go with the methods that are already present and don't use science as an excuse to postpone any changes.
- ScienceDirect: Mitigation of methane and nitrous oxide emissions from drained irrigated rice fields
- World Resource Institute: More Rice, Less Methane
- World Resource Institute: Wetting and Drying: Reducing Greenhouse Gas Emissions and Saving Water from Rice * Production
- Climate CoLab: Reducing methane emissions from rice farming
- ASB Partnership: Reducing Methane Emissions from Irrigated Rice [PDF]
- Civil Eats: Could Changing the Way We Farm Rice Be a Climate Solution?
- Nature: Rice, microbes and methane
- Nature: Cable bacteria reduce methane emissions from rice-vegetated soils