Purpose To accelerate coronary MRI acquisitions with arbitrary undersampling patterns by using a novel reconstruction algorithm that applies coil self-consistency using subject-specific neural networks. Methods Self-consistent robust artificial-neural-networks for k-space interpolation (sRAKI) performs iterative parallel imaging reconstruction by enforcing self-consistency among coils. The approach bears similarity to SPIRiT, but extends the linear convolutions in SPIRiT to nonlinear interpolation using convolutional neural networks (CNNs). These CNNs are trained individually for each scan using the scan-specific autocalibrating signal (ACS) data. Reconstruction is performed by imposing the learned self-consistency and data-consistency, which enables sRAKI to support random undersampling patterns. Fully-sampled targeted right coronary artery MRI was acquired in six healthy subjects. The data were retrospectively undersampled, and reconstructed using SPIRiT, l₁-SPIRiT and sRAKI for acceleration rates of 2 to 5. Additionally, prospectively undersampled whole-heart coronary MRI was acquired to further evaluate reconstruction performance. Results sRAKI reduces noise amplification and blurring artifacts compared with SPIRiT and l₁-SPIRiT, especially at high acceleration rates in targeted coronary MRI. Quantitative analysis shows that sRAKI outperforms these techniques in terms of normalized mean-squared-error (~44% and ~21% over SPIRiT and ‘₁-SPIRiT at rate 5) and vessel sharpness (~10% and ~20% over SPIRiT and l₁-SPIRiT at rate 5). Whole-heart data shows the sharpest coronary arteries when resolved using sRAKI, with 11% and 15% improvement in vessel sharpness over SPIRiT and l₁-SPIRiT, respectively. Conclusion sRAKI is a database-free neural network-based reconstruction technique that may further accelerate coronary MRI with arbitrary undersampling patterns, while improving noise resilience over linear parallel imaging and image sharpness over l₁ regularization techniques.