Motor noise

[m_c]

Just to clarify, is the relay coil powered by AC or DC?

For this bit, I'm going to assume AC, as DC switching SSR's aren't that common.
Can you not power the coolant pump direct from the SSR?
A coolant pump isn't likely to draw any more than an amp or so while running (any coolant pumps I've seen are only 1/3hp), although there will be a bit higher of a surge during startup.
Also, I would try only switching the Live, so that the motor winding is still connected to something as it slows down.

[M250cnc]

Hi and thanks, the relay coil is powered 12VDC

Good point about the live only switching

Phil