The issue is that the arrange marriage window excludes all the random women in each court to cut down on size. Thats not a big deal if you are a noble, but is a problem if you are a patrician.
As a patrician, learn to simply ignore the arrange marriage window. Instead do a a character search (female, married = no, ruler = no, my culture (optional), my religion) and arrange marriages through that. Not as easy, but gives more variety.
Using various methods to invite high ranking noble women and marrying them in your court, therefore avoiding dowry is also a standard patrician tactic.