Yes, there are.
In fact, in this paper by LeBrun and Mason, they refer to a result by Guillemin 1976 according to which for any odd smooth function $f:S^2\to \mathbb{R}$, there is a one-parameter family $g_t=\exp(f_t)g_0$ of smooth Zoll metrics with $g_0$ the round one and $(df_t/dt)_{t=0}=f$.
If $f$ is not rotationally symmetric, you have examples.
Lebrun and Mason classify instead Zoll projective structures by very nice twistor-like constructions.
ADDED: Guillemin's result is detailed in A. Besse "Manifolds all of whose geodesics are closed", p.126 theorem 4.70.