I don't know if an automatic/magnetic doggy door is an option for you, but here's a link. (I'm not endorsing this product since I know nothing about it, but it may be something you can look into).
I have heard of people trying citrus around the door, which is supposed to deter cats because they don't like the citrus scent. I'm not sure how effective it is.
ETA: Forgot the link.
Electronic and Automatic Pet Doors