New Transformer possible?

You would need to know exactly what the voltages on the wires coming out are supposed to be, and how many amps each is to be capable of supporting.
Then to find a transformer with the same specs (you can go for more capacity on the amps, but the voltages have to be the same.) Usually bigger is better, smaller i would be leary of (in general)
Have you tried to tighten down the tranny? another possiblity is to build a muffler for it. A cover than would reduce the levels of sound, but allow it to cool at the same time. If it is in a case already, perhaps potting it. filling the case with something? A product that would quiet it and transfer heat out.
Good luck.

For a quick fix, take two "C" clamps, and clamp down each side of the steel plates that make up the 'iron' of the transformer. See if that quiets it down. If yes, you could have a clamp made (or make one yourself) to do the same thing in a more discrete manner.
Usually it is the laminate plates (the iron) that get loose and buzz. They use a shellac to glue them together, and age and deterioration breaks the bonds. No problem for the transformer, just for your ears.
Clamping the plates should make it quiet.

Elizabeth,thankyou for the advice I will give everything a try and let you know.How do you go about making a muffler, it is something I thougth about,but really have know idear how to make one.Thanks Maxwell

For a quick fix, take two "C" clamps, and clamp down each side of the steel plates that make up the 'iron' of the transformer.

If you go clamping around on an E-I core transformer, be sure to add insulation (i.e. a plastic washer) under one side of the clamp! This will prevent the possibility of stumbling across a configuration whereby the clamp shorts out the magnetic circuit.