The regularized kernel methods for ranking problem have attracted increasing attention recently, which are usually based on the regularization scheme in a reproducing kernel Hilbert space. In this paper, we go beyond this framework by investigating the generalization ability of ranking with coefficient-based regularization. A regularized ranking algorithm with a data-dependent hypothesis space is proposed and its representer theorem is proved. The generalization error bound is established in terms of the covering numbers of the hypothesis space. Different from the previous analysis relying on Mercer kernels, our theoretical analysis is based on much general kernel function, which is not necessarily symmetric or positive semi-definite. Empirical results on the benchmark datasets demonstrate the effectiveness of the coefficient-based algorithm.