Well, i'm a bit unclear which coil you're referring to but anyway: i think this tv has an Avant chassis.
I also think you're not annoyed by the 15KHz noise as any crt tv has this 'whistle' but weak and high so barely/not audible for the 'grown-up' ear, but sometimes one of the linearity coils or deflection coil or HT transformer may start to whistle/resonate at a much lower freqency.
If it's one of the smaller coils or HT transformer sometimes sodlering a few of the connections while pushing it a bit sideways may help (to change the 'phisycal tension') or sometimes maybe a tie-wrap arond it.
There's no 'miracle cure' just like that, it's a bit of trial and error or....just order a new one and replace :)