High-precision manipulation has always been a developmental goal for aerial manipulators. This paper investigates the kinematic coordinate control issue in aerial manipulators. We propose a predictive kinematic coordinate control method, which includes a learning-based modified kinematic model and a model predictive control (MPC) scheme based on weight allocation. Compared to existing methods, our proposed approach offers several attractive features. First, the kinematic model incorporates closed-loop dynamics characteristics and online residual learning. Compared to methods that do not consider closed-loop dynamics and residuals, our proposed method has improved accuracy by 59.6$\%$. Second, a MPC scheme that considers weight allocation has been proposed, which can coordinate the motion strategies of quadcopters and manipulators. Compared to methods that do not consider weight allocation, the proposed method can meet the requirements of more tasks. The proposed approach is verified through complex trajectory tracking and moving target tracking experiments. The results validate the effectiveness of the proposed method.