Context. There is a class of binary post-asymptotic giant branch (post-AGB) stars that exhibit remarkable near-infrared (NIR) excess. Such stars are surrounded by Keplerian or quasi-Keplerian disks, as well as extended outflows composed of gas escaping from the disk. This class can be subdivided into disk-and outflow-dominated sources, depending on whether it is the disk or the outflow that represents most of the nebular mass, respectively. The chemistry of this type of source has been practically unknown thus far. Aims. Our objective is to study the molecular content of nebulae around binary post-AGB stars that show disks with Keplerian dynamics, including molecular line intensities, chemistry, and abundances. Methods. We focused our observations on the 1.3, 2, 3 mm bands of the 30 m IRAM telescope and on the 7 and 13 mm bands of the 40 m Yebes telescope. Our observations add up ∼ 600 hours of telescope time. We investigated the integrated intensities of pairs of molecular transitions for CO, other molecular species, and IRAS fluxes at 12, 25, and 60 µm. Additionally, we studied isotopic ratios, in particular 17 O / 18 O, to analyze the initial stellar mass, as well as 12 CO / 13 CO, to study the line and abundance ratios.Results. We present the first single-dish molecular survey of mm-wave lines in nebulae around binary post-AGB stars. We conclude that the molecular content is relatively low in nebulae around binary post-AGB stars, as their molecular lines and abundances are especially weaker compared with AGB stars. This fact is very significant in those sources where the Keplerian disk is the dominant component of the nebula. The study of their chemistry allows us to classify nebulae around AC Her, the Red Rectangle, AI CMi, R Sct, and IRAS 20056+1834 as O-rich, while that of 89 Her is probably C-rich. The calculated abundances of the detected species other than CO are particularly low compared with AGB stars. The initial stellar mass derived from the 17 O / 18 O ratio for the Red Rectangle and 89 Her is compatible with the central total stellar mass derived from previous mm-wave interferometric maps. The very low 12 CO / 13 CO ratios found in binary post-AGB stars reveal a high 13 CO abundance compared to AGB and other post-AGB stars. Key words. stars: AGB and post-AGB − binaries: general − circumstellar matter − radio lines: stars − ISM: planetary nebulae: general ⋆ Based on observations with the 30 m IRAM and the 40 m Yebes telescopes. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain).⋆⋆ Final spectra are available at the CDS via anonymous FTP to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/gcat?J/A+A/ 1 We follow the recommendations for units of the IAU Style Manual (Wilkins 1990(Wilkins , 1995. Therefore, we use the term annus, abbreviated as "a", for year. type stars with C/O < 1, the S-type stars with C/O ≈ 1, and Ctype with C/O > 1. The kind of molecules and dust grains found in CSEs is determined by the C/O ratio. We find O-bearing molecules, such...