vintagemotif,
The Necchi BU machines can be treadled, but you have to drill out the holes for hinge pins if you drop it into a Singer cabinet.
The Singer 319 just needs a motorectomy to treadle, I treadle a Singer 15-90 and its sews beautifully. Some other machines with the external motor can be converted to treadle use as long as the handwheel has a deep belt groove.
I have discovered that the Singer 237m was offered as either an electric or treadle machine in Italy, where it was made.