Coronary MRI is a non-invasive radiation-free imaging tool for the diagnosis of coronary artery disease. One of its limitations is the long scan time, due to the need for high resolution imaging in the presence of respiratory and cardiac motions. Machine learning (ML) methods have been recently utilized to accelerate MRI. In particular, a scan-specific ML technique, called Robust Artifical-neural-network for k-space Interpolation (RAKI) has shown promise in cardiac MRI. However, it requires uniform undersampling. In this study, we sought to extend this approach to arbitrary sampling patterns, using coil self-consistency. This technique, called SPIRiT-RAKI, utilizes scan-specific convolutional neural networks to nonlinearly enforce coil self-consistency. Additionally, regularization terms can also be incorporated. SPIRiT-RAKI was used to accelerate right coronary MRI. Reconstructions were compared to SPIRiT for different undersampling patterns and acceleration rates. Results show SPIRiT-RAKI reduces residual aliasing and blurring artifacts compared to SPIRiT.