If anyone reading this keeps garden doves in a dovecote and is having problems with predators, I would recommend keeping them in an aviary instead.
This is how I reduced the attacks, although sadly have not eliminated them. The aviary has 2 flight holes that enable the birds to go in and out freely.
It is also possible to close the flight holes during times of increased attacks. The protective environment also allows the squabs to leave the nest and be fed on the ground safely by their parents, without risk from cats or other predators.