Of these three types of methane gas, thermogenic and abiogenic are not renewable, insomuch as we don't know how many more dinosaurs or molecules are left to putrefy below the Earth's surface. Also, drilling in the Earth to reap this resource is extremely expensive.
On the other hand, biogenic methane is sustainable. The microorganisms that create this type of methane are simply doing what comes naturally. The United States Department of Agriculture has organized more than 100 projects since 2003 to collect biomethane from cow manure. All that manure saved 8 million gallons of oil. In fact, most biofuel in the United States was obtained from cow manure.
In landfills, the power of garbage decomposition can be harnessed to reap natural gas, since the methanogens that eat the organic garbage in dumps produce methane. As long as humans (and cows) keep producing organic, biogenic methane, or biomethane, it will always be renewable.