The intensity profiles of the C2 Swan bands in cool DQ white dwarfs cannot be adequately fitted with models that otherwise succesfully reproduce spectral features of the molecule CH in these stars. Initial modelling showed that a two-component atmosphere in the style of a spot might be able to solve the problem. We photometrically observed the two cool DQ white dwarfs GJ1117 and EGGR78 to search for variability caused by stellar spots. We have not found any such variability, but we estimate the effects of hypothetical spots on lightcurves. We also estimate detection probabilities for spots in different configurations. Alternative explanations of the problem are needed and briefly discussed.