Traditionally, 10% dimethyl sulfoxide (DMSO) has been used for -80C long-term storage of methanotrophs. However, various labs have had success storing methanotrophs in other cryoprotectants such as glycerol, PEG, or trehalose. Other labs have placed cells on filter paper for -80C storage. Some have even lyophilized cultures for long-term storage. The rule of thumb is to find the protocol that works best in your hands and stick with that method. The following references discuss several methods for long-term preservation:
Doronina, N. V.; Trotsenko, Y.A. 1992. Method for storage of methylotrophic and heterotrophic microorganisms. Prikladnaya Biokhimiya I Mikrobiologiya. 28(4): 631-635
Hoefman, S., Van Hoorde, K., Boon, N., Vandamme, P., De Vos, P., and Heyle, K. 2012. Survival or Revival: Long-Term Preservation Induces a Reversible Viable but Non-Culturable State in Methane-Oxidizing Bacteria. 7(4): e34196.