This paper solves the problem of spacecraft rendezvous with input delay by designing the periodic event triggered control (PETC) and periodic self-triggered control (PSTC), respectively. Firstly, a PETC based on the discrete-time parametric Lyapunov equation (DPLE) is designed to stabilize the delayed spacecraft rendezvous systems. Moreover, in order to avoid monitoring the measurement errors, a PSTC algorithm that the updates of the next control law depend on the previous triggered states is also designed. Specially, by using the properties of the DPLE, this new approach is not only simple, but also provides an easy and explicit condition on the only parameter of DPLE to guarantee the non-triviality of the designed PETC and PSTC. Finally, the effectiveness of theoretical results is verified by simulations.