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This paper addresses the co-design of event-triggered dynamic output-feedback (DOF) control for discrete-time linear parameter-varying (LPV) systems. Two independent event-triggering schemes are introduced to determine when to transmit data from the sensor to the controller and from the controller to the actuator channels. Enhanced conditions employing linear matrix inequalities (LMIs) are derived to establish constructive criteria for simultaneously designing the gain-scheduled DOF controller and the triggering mechanisms, ensuring the asymptotic stability of the closed-loop LPV system's origin. Additionally, a convex optimisation problem is proposed to enlarge the inter-event sampling on the independent channels of sensor-to-controller and controller-to-actuator. Numerical examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]