The γ-ray emissions from a radiopure cerium-bromide crystal with a mass of 4381 g were measured for a total of 497.4 d by means of high-resolution γ-ray spectrometry in the HADES underground laboratory at a depth of 500 m.w.e. A search for 0/2νϵϵ and 0/2νϵβ+ double beta decay transitions of Ce136 and Ce138 was performed using Bayesian analysis techniques. No signals were observed for a total of 35 investigated decay modes. 90% credibility limits were set in the order of 1018-1019 yr. Existing constraints from a cerium oxide powder measurement were tested with a different cerium compound and half-life limits could be improved for most of the decay modes. The most likely accessible decay mode of the Ce136 2νϵϵ transition into the 01+ state of Ba136 results in a new best 90% credibility limit of 5.0×1018 yr.