  We present the results of a search for high-energy gamma-ray emission from a
large sample of galaxy clusters sharing the properties of three existing
Fermi-LAT detections (in Perseus, Virgo and Abell 3392), namely a powerful
radio source within their brightest cluster galaxy (BCG). From a parent, X-ray
flux-limited sample of clusters, we select 114 systems with a core-dominated
BCG radio flux above 50 or 75 mJy, stacking data from the first 45 months of
the Fermi mission, to determine statistical limits on the gamma-ray fluxes of
the ensemble of candidate sources. For a >300 MeV selection, the distribution
of detection significance across the sample is consistent with that across
control samples for significances <3 sigma, but has a tail extending to higher
values, including three >4 sigma signals which are not associated with
previously identified gamma-ray emission. Modelling of the data in these fields
results in the detection of four non-2FGL Fermi sources, though none appear to
be unambiguously associated with the BCG candidate. A search at energies >3 GeV
hints at emission from the BCG in A 2055, which hosts a BL Lac object. There is
no evidence for a signal in the stacked data, and the upper limit derived on
the gamma-ray flux of an average radio-bright BCG in the sample is an
order-of-magnitude more constraining than that calculated for individual
objects. F(1 GeV)/F(1.4 GHz) <15, compared with ~120 for NGC 1275 in Perseus,
which might indicate a special case for those objects detected at high
energies; that beamed emission from member galaxies comprise the dominant
bright gamma-ray sources in clusters.
