The majority of remote locations not connected to the main electricity grid rely on diesel generators to provide electrical power. High fuel transportation costs and significant carbon emissions have motivated the development and installation of hybrid power systems using renewable energy such these locations. Because wind and solar energy is intermittent, such sources are usually combined with energy storage for a more stable power supply. This paper presents a modelling and sizing framework for off-grid hybrid power systems using airborne wind energy, solar PV, batteries and diesel generators. The framework is based on hourly time-series data of wind resources from the ERA5 reanalysis dataset and solar resources from the National Solar Radiation Database maintained by NREL. The load data also include hourly time series generated using a combination of modelled and real-life data from the ENTSO-E platform maintained by the European Network of Transmission System Operators for Electricity. The backbone of the framework is a strategy for the sizing of hybrid power system components, which aims to minimise the levelised cost of electricity. A soft-wing ground-generation-based AWE system was modelled based on the specifications provided by Kitepower B.V. The power curve was computed by optimising the operation of the system using a quasi-steady model. The solar PV modules, battery systems and diesel generator models were based on the specifications from publicly available off-the-shelf solutions. The source code of the framework in the MATLAB environment was made available through a GitHub repository. For the representation of results, a hypothetical case study of an off-grid military training camp located in Marseille, France, was described. The results show that significant reductions in the cost of electricity were possible by shifting from purely diesel-based electricity generation to an hybrid power system comprising airborne wind energy, solar PV, batteries and diesel.