COM frame for photons We know that there is no frame in which the energy of a photon is zero and hence it has zero momentum.
But can we find a frame in which the energy of two head on photons is zero, or the center of mass frame for two head on collision photons having different energies?
 A: No number of photons can have zero total energy in any frame, because energy is a scalar, and photon energies add up to a non-zero amount. A system of more than one photon can have net zero $momentum$ in the center-of-mass frame.
Formally, if two photons of different energies have 4-momenta in natural units given by $\tilde{p_1} = (E_1, \vec{p_1})$ and $\tilde{p_2} = (E_2, \vec{p_2})$ respectively in the frame moving along with the center of mass, the combined 4-momentum is $\tilde{p_1} + \tilde{p_2} = (E_1 + E_2, \vec{0})$ since $\vec{p_1} + \vec{p_2}=0$ in said frame. Note that the total energy is simply the sum of the COM energies.
A: 
We know that there is no frame in which the energy of a photon is zero and hence it has zero momentum.

Correct.

But can we find a frame in which the energy of two head on photons is zero [?]

No, that's not possible. You cannot transform away the relative kinetic energy like that. However, there is an inertial frame where the total momentum of the two photons is zero. That's true for any two photons that aren't heading in exactly the same direction. That works because momentum is a vector. It doesn't work for energy, because energy is a scalar.
