Pigeon-fancying — to which this word refers — was especially strong in England in the nineteenth century, with great skill expended in breeding new varieties for show. Charles Darwin became a fancier in 1855 to study variation within species as part of his research which became On the Origin of Species.
Like other bodies of the period, pigeon-fanciers’ societies looked to the classical languages for suitably distinguished titles. At the time Darwin became involved, a London one was grandly called the Philoperisteron Society. Philo- means a lover of something, from Greek philos, loving; peristeron was invented by a learned founder, which he took from Greek peristera for a wild pigeon or dove. The organisation changed its name in 1867 to the National Peristeronic Society (which still exists), in which peristeronic was another invented word, an adjective with the sense “relating to or concerned with pigeons”. The change of name should not be taken as meaning that the members of the society had ceased loving their pigeons.
Another organisation of the time was the Columbarian Society, whose name is from Latin columbarius, a keeper of doves. The related columbarium could mean a dovecote or pigeon loft, but it now refers to a place in a crematorium where urns holding a deceased’s cremated remains are stored; the connection is that the niches for the urns in a columbarium reminded people of roosting holes in a dovecote. Several societies retain columbarian in their names, including the National Columbarian Society in the USA.
[Thanks to Richard Thomas for telling me about peristeronic.]