Every other CAD system I have used allows you to select a plane and a cylinder and constrain it coincidentally. The assumed axis of the cylinder is used. I even tried creating an reference axis from the cylinder I want to align. It won't let me select the axis and a plane in the constraint tool. Seems like pretty basic functionality.
Turn on temporary axes and you should be able to use the axis from the cylinder. Some people seem to shy away from using temporary axes but they've always worked fine for me.