Understanding atomic-level mechanisms of methane adsorption in nanoporous materials is of great importance to increase their methane storage capacity targeting energy sources with low carbon emission. In this work, we considered layered covalent organic frameworks (COFs) with low density and revealed the effect of slipping and chemical functionalization on their methane adsorption and separation properties. We performed grand canonical Monte Carlo simulations studies of methane (CH4) adsorption and carbon-dioxide:methane (CO2:CH4) separation in various slipped structures of TpPa1, TpBD, PI-COFs, and functionalized TpPa1 and TpBD COFs as well. We observed that the slipping improves the total CH4 uptake by 1.1-1.5 times, while functionalization does not have a significant effect on CH4 uptake. We also observed improvement in CO2:CH4 selectivity due to slipping, whereas functionalization results in decrease in the selectivity. In all considered COFs, we found the highest CH4 delivery capacity of 141 cm3 (STP) cm-3 at 65 bar and selectivity of ∼25 at 1 bar in 60-AB slipped structure of TpBD COF. We analyzed the molecular details of CH4 adsorption using binding energy, heat of adsorption, pore characteristics, and expectation energy landscape. Our results show that COFs with increasing profile of heat of adsorption with pressure have the higher CH4 delivery capacity. In these COFs, we found proximity (∼4-6 Å) of CH4 binding sites, resulting in higher CH4-CH4 interactions and hence the increasing profile of CH4 heat of adsorption.