As I recall, the cotoneaster in my mother's garden in BC was very popular with the birds when the berries were on it. She did used to see small seedlings under the larger bushes there.
Perhaps the seed is a type that needs to pass through the gut of a critter before it will germinate?
Rather than wait for birds to eat your seeds then trying to collect them . . .
(just kidding) maybe fermenting them (as seed savers do for tomatoes) will help speed up the process? Mash up a few ripe berries, add a little water and maybe a touch of sugar, put it some place warm-ish, let it get stinky, then try planting the seeds.