  We consider the optimal cloning of quantum coherent states with single-clone
and joint fidelity as figures of merit. Both optimal fidelities are attained
for phase space translation covariant cloners. Remarkably, the joint fidelity
is maximized by a Gaussian cloner, whereas the single-clone fidelity can be
enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can
achieve a single-clone fidelity of approximately 0.6826, perceivably higher
than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can
be realized by means of an optical parametric amplifier supplemented with a
particular source of non-Gaussian bimodal states. Finally, we show that the
single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a
measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a
Gaussian scheme and cannot be surpassed even with supplemental bound entangled
states.
