You would need at least a 50V coil circuit which system 3-7 does not have.

You could at least try with the 30V that Flash has. Especially if it doesn't need to go as high as some VUKs do. As far as the circuit, the hardest part would be giving it a delay for the ball to settle. You'd probably need a timer circuit to trigger the coil.

A 4017 CMOS DEVICE [or a micro controller], A 12 VOLT REGULATOR AND RELAY/*Transistor .
With the 4017 you can make a sequence...to continually pulse [eg 1 sec ...2secs] the relay if switch is pushed.This will give you a timer to make sure the ball has settled a kickout pulse and the ability to retrigger if it didnt eject.

The regulator to knock the 30 volts down to 12v for the circuit.

The relay operates the coil which at 30v maybe use a 3.5 ohm ....a bumper coil say(the voltage is errelavant its the power equation).
Volts X Current = Power(watts)
Volts/impedance = current
eg... 10v/10 ohms = 1 amp..... 10V X 1 Amp = 10 Watts
Later model machines run on 50 Volts to lower the current flow thru the system this does not however change the overall power consumption.

Using a dual pole 10 amp relay will allow you to have one pole wired across an existing
switch on the playfield to enable sound and/or scoring.
....all garden variety parts.

pls note; switching DC voltages over 30 volts with a relay can have issues with releasing the load, a good quality relay would be required.
*A drive transistor could replace the relay in the above situation just as easily though not as versatile.

i like the idea you've got , PM me and i can send you circuit.

.......in the time it took me to type this i could have built the thing.

In simpler terms, yes you can, it would cost about $ 30 for you to do it.