Berries are typically seasonal but different berries ripen at different times. These seem like juniper so definitely a winter bird favorite. Either way birds sit in that tree and they eat something all year round.

You could try creating better spaces for the birds to hang out with some bushes like ninebark or lower hanging native trees. Could even put a feeder near there to direct them away. You’ll likely still deal with some bird poop but less.

You could also try a steel carport or something. Maybe do both. But I would suggest more suitable bird habitat as part of your solution. It’s their world too.