Do you know anybody really handy? Is it a finished table? If it's just plywood or the sort, someone could cut pieces & glue/toenail them in. The easiest thing would be to cut a whole new top using the machine base for a pattern for the opening & screw it on top. It should be painted with enamel or varnished for the fabric to slide easily over it.

I bought a cabinet at an auction one time & my machine didn't fit either.

I have my White on top of an old Singer treadle cabinet. The old machine is down in the hole and my machine sits on top. DH cut me a piece of thin plywood to exactly fit the hole so it's flush. When the machine is set up on it, you can't really see the plywood at all. Works great for me because I never want to put the machine away. If you were wanting it to swing down, that would certainly be more complicated and might involve a machinist who works with metal.

Tootsie,
Something like this is what you need, but unfortunately I don't know where you would get it. When I bought a mid-80's Singer(in the mid-80's,LOL), the(fabric)store sold me a universal table and this plastic extension to go with it. It sets on the table in back of the machine, taking up the extra space. My Singer is long gone, but I still use this extension with my current machine(which is taller, but the extension is still usable). I don't know who manufactured the table, but maybe the info on the extension will help you with some research.