  We study the spin-1/2 XXZ model on the triangular lattice with a nearest
neighbor antiferromagnetic Ising coupling $J_z>0$ and unfrustrated
($J_\perp<0$) or frustrated ($J_\perp>0$) kinetic terms in zero magnetic field.
Incorporating long-range Jastrow correlations over a mean field spin state, we
obtain the variational phase diagram of this model on large lattices for
arbitrary $J_z$ and either sign of $J_\perp$. For $J_\perp<0$, we find a
$\sqrt{3}\times\sqrt{3}$ supersolid for $J_z/|J_\perp| \gtrsim 4.7$, in
excellent agreement with quantum Monte Carlo data. For $J_\perp >0$, a distinct
$\sqrt{3}\times\sqrt{3}$ supersolid is found to emerge for $J_z/J_\perp \geq
1$. Both supersolids exhibit a spontaneous density deviation from half-filling.
At $J_z/J_\perp=\infty$, the crystalline order parameters of these two
supersolids are nearly identical, consistent with exact results.
