Why does she need a manual? Old machines like that are very easy to use, oil, clean, etc. without one. I often buy machines like that in thrift stores to fix up for a local non-profit and really don't need a manual to get them cleaned, oiled and running for use. If she still really wants a manual, any manual for a Singer Fashionmate would work. Here is a link to manuals for sale that include the Fashionmate:
http://www.sewusa.com/Sewing_Machine...ng_Machine.htm
I clicked on the Fashionmate 360 and the diagram of the machine looks very much like your sister's machine.