You risk puncturing the tube with a tire lever sometimes, one way I found with the super hard ones is too get it on the best you can with your hands, then afterwords back the bead off the lip in one direction and pop the part your were previously struggling with on, the new section that isnt on the tube should be out of the way and you can use a tire lever to muscle the rest on.. not fool proof but Ive had success with it.

I think modern tires dont work so good with our vintage rims cause they are usually 4-5mm wider than the new stuff modern tires are probably built around.