Context. It is now clear that binarity plays a crucial role in many aspects of planetary nebulae (PNe), particularly the striking morphologies that they show. To date, there are ∼ 60 bCSPNe known. However, both theory and observation indicates that this represents only the tip of the iceberg, with the Galactic PN population hosting orders of magnitude more. Aims. We are involved in a search for new bCSPNe to enhance the statistical validation of the key role of binarity in the formation and shaping of PNe. New discoveries of bCSPNe and their characterization have important implications not only in understanding PN evolution but also in understanding binary evolution and the poorly-understood common-envelope phase. Methods. We used data from the TESS satellite to search for variability in the eight CSPNe that belong to the two-minute cadence preselected targets in Cycle 1, which have available pipeline-extracted light curves. We identified strong periodicities and analysed them in the context of the binary scenario. Results. All the CSPNe but one (Abell 15) show clear signs of periodic variability in TESS. The cause of this variability can be attributed to different effects, some of them requiring the presence of a companion star. We find simple sinusoidal modulations in several of the systems, compatible to irradiation effects. In addition, two of the central stars (PG 1034+001 and NGC 5189) also show photometric variations due to ellipsoidal variations and other signs of variability probably caused by star spots and/or relativistic Doppler-beaming. Especially interesting is the case of the well-studied Helix Nebula, in which we constructed a series of binary models to explain the modulations we see in the light curve. We find that the variability constrains the possible companion to be very low-mass main-sequence star or sub-stellar object. We also identify with a great detail the individual pulsation frequencies of NGC 246.