In this second paper on our variability survey of central stars of planetary nebulae (CSPNe) using the Zwicky Transient Facility (ZTF), we report 11 long-timescale variables with variability timescales ranging from months to years. We also present preliminary analyses based on spectroscopic and/or photometric follow-up observations for six of them. Among them is NGC 6833, which shows a 980 days periodic variability with strange characteristics: "triangle-shaped" brightening in r, i, and WISE bands but almost coincidental shallow dips in the g-band. The most plausible explanation is a wide binary with the photometric period being the orbital period. Long-period near-sinusoidal variability was detected in two other systems, NGC 6905 and Kn 26, with periods of 700 days and 230 days, respectively, making them additional wide-binary candidates. The latter also shows a short period at 1.18 hr. We then present CTSS 2 and K 3-5, which show brightening and significant reddening over the whole ZTF baseline. A stellar model fit to the optical spectrum of CTSS 2 reveals it to be one of the youngest post-AGB CSPNe known. Both show high-density emission-line cores. We propose these to be late-thermal-pulse candidates, currently evolving towards the AGB phase. We then present recent HST/COS ultraviolet spectroscopy of the known wide-binary candidate LoTr 1, showing that the hot star is a spectroscopic twin of the extremely hot white dwarf in UCAC2 46706450. Similar to this object, LoTr 1 also has a fast rotating wide subgiant companion. We suggest that the long photometric period of 11 yr is the binary orbital period. Finally, we briefly discuss the ZTF light curves of the remaining variables, namely Tan 2, K 3-20, WHTZ 3, Kn J1857+3931, and IPHAS J1927+0814. With these examples, we present the effectiveness of the von Neumann statistics and Pearson Skew-based metric space in searching for long-timescale variables. *Based in part on observations obtained with the Hobby-Eberly Telescope (HET), which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Ludwig-Maximillians-Universität München, and Georg-August Universität Göttingen. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly.