They look a lot like Harman Kardon A-224 and T-224 but for the red pilot lamps on the top/center of each. Those could have been prop-added though. What is weird about that shot is how shallow the shelves look; it makes me wonder if the whole rig was a prop. The record changer looks vaguely Voice of Music-ish.
If you liked that movie, check out the original novel. O'Hara set it in the 30s (when he wrote it) and you can tell he was very much into popular music. Lots of references to the songs of the day, most of which have faded into obscurity.
Of course the novel lacks the most appealing aspect of the film. In 1960 Liz Taylor was about the sexiest thing on wheels.