It's very difficult to consume dairy without animals being killed, because cows need to be pregnant to produce milk, which has the side-effect of more cows. In industrial production, we're talking roundabout 5 calves over the lifetime of 1 milk cow. Those calves are not being kept around.
You'd need to find a farmer that only milks their cows when they get pregnant naturally.

With eggs, backyard chickens can be argued to be moral (given humane conditions). But industrial production involves male chicks being shredded and horrendous conditions for those that get to live.

In either case, I'd consider a vegan diet with supplements so much easier.