Cooperative communication through energy harvested relays in Cognitive Internet of Things (CIoT) has been envisioned as a promising solution to support massive connectivity of Cognitive Radio (CR) based IoT devices and to achieve maximal energy and spectral efficiency in upcoming wireless systems. In this work, a cooperative CIoT system is contemplated, in which a source acts as a satellite, communicating with multiple CIoT devices over numerous relays. Unmanned Aerial Vehicles (UAVs) are used as relays, which are equipped with onboard Energy Harvesting (EH) facility. We adopted a Power Splitting (PS) method for EH at relays, which are harvested from the Radio frequency (RF) signals. In conjunction with this, the Decode and Forward (DF) relaying strategy is used at UAV relays to transmit the messages from the satellite source to the CIoT devices. We developed a Multi-Objective Optimization (MOO) framework for joint optimization of source power allocation, CIoT device selection, UAV relay assignment, and PS ratio determination. We formulated three objectives: maximizing the sum rate and the number of admitted CIoT in the network and minimizing the carbon dioxide emission. The MOO formulation is a Mixed-Integer Non-Linear Programming (MINLP) problem, which is challenging to solve. To address the joint optimization problem for an epsilon optimal solution, an Outer Approximation Algorithm (OAA) is proposed with reduced complexity. The simulation results show that the proposed OAA is superior in terms of CIoT device selection and network utility maximization when compared to those obtained using the Nonlinear Optimization with Mesh Adaptive Direct-search (NOMAD) algorithm.