The suppression of secondary electron yield (SEY) which can possibly lead to multipactor is an important goal for several applications. Though some techniques have focused on geometric modifications to lower the SEY, the use of graphene coatings as thin as a few monolayers is a promising new development that deserves attention either as a standalone technique or in concert with geometric alterations. Here we report on Monte Carlo based numerical studies of SEY on graphene coated copper with comparisons to recent experimental data. Our predicted values are generally in good agreement with reported measurements. Suppression of the secondary electron yield by as much as 50 percent (over copper) with graphene coating is predicted at energies below 125 eV, and bodes well for multipactor suppression in radio frequency applications.