This paper investigates the application of the steered response power - phase transform (SRP-PHAT) method to coprime microphone array (CPMA) recordings to estimate the direction of arrival (DOA) of speech sources. While existing CPMA approaches for acoustics applications are limited, especially under reverberant conditions, the proposed algorithm utilises SRP-PHAT to estimate the DOA of speech sources and then employs a histogram-based stochastic algorithm using steered response power (SRP) adjustment and kernel density evaluation (KDE) to improve the DOA estimation accuracy. Experiments are conducted for up to three simultaneous speech sources in the far field considering both anechoic and reverberant scenarios. Results suggest that the proposed approach achieves more accurate DOA estimates than a uniform linear array (ULA) with the same number of microphones under both anechoic and low reverberant conditions, and it significantly decreases the number of microphones of another equivalent ULA while maintaining similar performances. Moreover, the operating frequency of the microphone array is largely increased without changing the number of microphones, making it possible to accurately record higher-frequency components of source signals.