Context: γ Dor stars are excellent targets for asteroseismology since the gravity modes present in these stars probe the deep stellar interiors. Mode identification will improve the knowledge of these stars considerably. Aims: A selected group of γ Dor stars and some candidates were observed with the Mercator telescope to find and/or confirm the periodicities in the light variations and to derive reliable amplitude ratios in different pass bands. Methods: A frequency analysis was performed on all new data obtained in the Geneva photometric system. In order to have more reliable and accurate frequencies, the new data were combined with similar data from the literature and with Hipparcos observations. A set of frequencies that minimized the residuals in a harmonic fit was searched for while allowing means and amplitudes to vary from one observation set to another. Results: Frequencies and amplitudes in the photometric passbands of the Geneva system are given for 21 γ Dor stars. We report the discovery of HD 74504 as a newly found γ Dor star. Conclusions: Our study provides the first extensive multicolour database for the understanding of gravity modes in F-type stars. Based on observations collected with the Flemish 1.2-m Mercator Telescope at Roque de los Muchachos, La Palma. Tables 5 to 25 are also 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/qcat?J/A+A/499/967