The Morse code transmission speed of the FSK identifiers of most translators I've installed is very slow, perhaps 2 or 3 WPM, so you will need a tuner with a DC-coupled discriminator output. Try connecting a scope (if the tuner has AFC, makes sure it's defeated) and look for the entire baseband audio waveform to shift up or down. Or find an old tuner with a center tuning meter and watch the pointer move to the side.
Instead of FSK, some translators send a "modulated CW" ID tone of approximately 1 kHz via ~ 30% amplitude modulation of the RF amplifier. FM receivers will usually limit this out if the input signal is strong enough for full quieting. However, you could probably copy it with a multimode receiver set for AM.