We designed 14 new covalent organic frameworks (COFs), which are expected to adsorb large amounts of methane (CH_4) at 298 K and up to 300 bar. We have calculated their delivery uptake using grand canonical Monte Carlo (GCMC) simulations. We also report their thermodynamic stability based on 7.5 ns molecular dynamics simulations. Two new frameworks, COF-103-Eth-trans and COF-102-Ant, are found to exceed the DOE target of 180 v(STP)/v at 35 bar for methane storage. Their performance is comparable to the best previously reported materials: PCN-14 and Ni-MOF-74. Our results indicate that using thin vinyl bridging groups aid performance by minimizing the interaction methane-COF at low pressure. This is a new feature that can be used to enhance loading in addition to the common practice of adding extra fused benzene rings. Most importantly, this report shows that pure nonbonding interactions, van der Waals (vdW) and electrostatic forces in light elements (C, O, B, H, and Si), can rival the enhancement in uptake obtained for microporous materials derived from early transition metals