My problem is that I want to make a third date-column that will use the dates from table beta if they are not null. If they are null, it should use the dates from table alpha.
Since you have not provided any info about your data model. I have given you a rough draft based on your problem.
Select colA, colB, ..., alpha.date1, beta.date2, COALESCE(beta.date2,alpha.date1) date3 from alpha left outer join beta (your keys)