Metal-organic frameworks (MOFs) are actively being explored as potential adsorbed natural gas storage materials for small vehicles. Experimental exploration of potential materials is limited by the throughput of synthetic chemistry. We here describe a computational methodology to complement and guide these experimental efforts. The method uses known chemical transformations in silico to identify MOFs with high methane deliverable capacity. The procedure explicitly considers synthesizability with geometric requirements on organic linkers. We efficiently search the composition and conformation space of organic linkers for 9 MOF networks, finding 48 materials with higher predicted deliverable capacity (at 65 bar storage, 5.8 bar depletion, and 298 K) than MOF-5 in 4 of the 9 networks. The best material has a predicted deliverable capacity 8% higher than that of MOF-5.