This paper takes a cursory look at the problem of inadequate power supply in the rural healthcare centres of a developing country, specifically Nigeria, and proffers strategies to address this issue through the design of hybrid renewable energy systems combined with the existing unreliable grid in order to meet the healthcare load demand, thus ensuring higher reliability of available energy sources. The simulations, analysis and results presented in this paper are based on meteorological data and the load profiles of six selected locations in Nigeria, using which hybrid grid-connected systems integrating diesel, solar and wind energy sources are designed with configurations to give optimum output. The optimised design configurations in the considered case study, Ejioku, Okuru-Ama, Damare-Polo, Agbalaenyi, Kadassaka and Doso, produce very low energy costs of of 0.0791 $/kWh, 0.115 $/kWh, 0.0874 $/kWh, 0.0754 $/kWh, 0.0667 $/kWh and 0.0588 $/kWh, respectively, leveraging solar and wind energy sources which make higher percentage contributions at all sites. The load-following-dispatch strategy is adopted at all sites, ensuring that at every point in time, there is sufficient power to meet the needs of the healthcare centres. Further works on this topic could consider other strategies to optimise general energy usage on the demand side.