How did protestant ministers respond to women's suffrage in the nineteenth century?

That depends which "Protestant ministers" you would have in mind.  Protestantism has wide disparities within its ranks, and not all were on the same page.  In the 19th century, most churches still stood against women's equality.  But movements toward women's suffrage included many Protestant women, and beginning in the late 19th century liberal Protestantism was more likely to be in support of such movements.  However, there remained (and still remain) many very conservative and traditional Protestant churches that are averse to giving women an equal role with men, basing their views on interpretations of Bible verses about men and women.  They've tended to acknowledge women voting in political society as a reality, but keep women in a secondary place within the church's organization.

Catholic leaders in the 19th century maintained that women's suffrage was "an affront to divine law and the natural order and a threat to family and society," according to Susan Hill Lindley in the book, You Have Stepped Out of Your Place: A History of Women and Religion in America (1996).