  We have developed capacitively-transduced nanomechanical resonators using
sp$^2$-rich diamond-like carbon (DLC) thin films as conducting membranes. The
electrically conducting DLC films were grown by physical vapor deposition at a
temperature of $500{\,\,}^\circ$C. Characterizing the resonant response, we
find a larger than expected frequency tuning that we attribute to the membrane
being buckled upwards, away from the bottom electrode. The possibility of using
buckled resonators to increase frequency tuning can be of advantage in rf
applications such as tunable GHz filters and voltage-controlled oscillators.
