If it is a Singer, I would think Singer needles would work since Singer has kept needle sizes consistent throughout all the varieties of machines since the 1890's.
Best bet would be to check out an older Singer repair website such as www.singer-featherweight.com or www.sewing-machines.blogspot.com and see if they have any information about the machine.
Another choice would be Lostn51 - Billy on this website. He specializes in vintage machines.