We investigate the dynamics of certain homeomorphisms F: T-2 -> T-2 of the form F(x, y) = (x + omega , h(x)+ f (y)), where omega is an element of R\Q, f: T -> T is a circle diffeomorphism with a unique (and thus neutral) fixed point and h: T -> T is a function which is zero outside a small interval. We show that such a map can display a non-uniformly hyperbolic behavior: (small) negative fibred Lyapunov exponents for a.e. (x, y) and an attracting non-continuous invariant graph. We apply this result to (projective) SL(2, R)-cocycles G: (x, u) bar right arrow (x + omega, A(x)u) with A(x) = R phi(x)B, where R-theta is a rotation matrix and B is a parabolic matrix, to get exam ples of non-uniformly hyperbolic cocycles (homotopic to the identity) with perturbatively small Lyapunov exponents.