The Kepler field hosts the best studied sample of field star rotation periods. However, due to Kepler's large 4 arcsecond pixels, many of its light curves are at high risk of contamination from background sources. The new Kepler Bonus Background light curves (Martinez-Palomera et al. 2023) are de-blended using a PSF algorithm, providing light curves of over 400,000 new background sources in addition to over 200,000 re-analyzed Kepler prime targets. These light curves provide the opportunity to search for new rotation periods. We present nearly 10,000 new periods for both Kepler prime and background sources, inferred by a convolutional neural network (CNN) trained on synthetic spot-modulated light curves. We also regressed nearly 20,000 periods from previously-measured sources and 600 pulsation frequencies from known asteroseismic oscillators, enabling the first robust validation of this CNN approach on real data. Examining the period distribution, we compare the periods and light curves of foreground-background pairs, finding that as many as 63% of periodic background light curves are still blended with the foreground. Finally, we highlight the regions of parameter space where the deblending is most and least effective for rotation, and we discuss exciting possible applications of this rich, new dataset.