This won't answer your direct query, but I have a reference which I feel may be useful to your wider quest. Your direct query I fear is going to be quite difficult, as the ability to beep upon an error is one of the more mundane parts of a machine's operation, so it likely to be relegated to operating manuals rather than written histories.

In particular, the 'bell' (or sometimes 'bel') character found in ascii (which was the easiest way to make a terminal go 'beep' right up until home computers got their own sound subsystems in the 80s), was inherited from Baudot in telegraphy and predates computers entirely. So the ability for operator terminals to reproduce this is going to be a very grey line. (I truly hope you get a more satisfying answer than this - if nothing else, for my own curiosity.)

In fact, it was Jack Dennis who suggested to [Peter] Samson that there were considerable uses for the capability of the TX-0 to send noise to the audio speaker. While there were no built-in controls for pitch, amplitude, or tone character, there was a way to control the speaker—sounds would be emitted depending on the state of the 14th bit in the 18-bit words the TX-0 had in its accumulator in a given microsecond. The sound was on or off depending on whether bit 14 was a 1 or 0. So Samson set about writing programs that varied the binary numbers in that slot in different ways to produce different pitches.

At that time, only a few people in the country had been experimenting with using a computer to output any kind of music, and the methods they had been using required massive computations before the machine would so much as utter a note. Samson, who reacted with impatience to those who warned he was attempting the impossible, wanted a computer playing music right away. So he learned to control that one bit in the accumulator so adeptly that he could command it with the authority of Charlie Parker on the saxophone. [..]

When outsiders heard the melodies of Johann Sebastian Bach in a single-voice, monophonic square wave, no harmony, they were universally unfazed. Big deal! Three million dollars for this giant hunk of machinery, and why shouldn’t it do at least as much as a five-dollar toy piano? It was no use to explain to these outsiders that Peter Samson had virtually bypassed the process by which music had been made for eons. Music had always been made by directly creating vibrations that were sound. What happened in Samson’s program was that a load of numbers, bits of information fed into a computer, comprised a code in which the music resided. You could spend hours staring at the code, and not be able to divine where the music was. It only became music while millions of blindingly brief exchanges of data were taking place in the accumulator sitting in one of the metal, wire, and silicon racks that comprised the TX-0. Samson had asked the computer, which had no apparent knowledge of how to use a voice, to lift itself in song, and the TX-0 had complied.

So it was that a computer program was not only metaphorically a musical composition — it was literally a musical composition! It looked like — and was — the same kind of program that yielded complex arithmetical computations and statistical analyses. These digits that Samson had jammed into the computer were a universal language that could produce anything — a Bach fugue or an antiaircraft system.

Levy, Steven. Hackers: Heroes of the Computer Revolution. Anchor Press/Doubleday, 1984.

I can't promise this book is the most scholarly work, but I've not heard its veracity much disputed either. It's highly regarded within the computing community, but Levy is a journalist more than a historian, and it shows in its presentation.

The TX-0, the machine described in this (a transistor-based, not chip-based, machine) was created in the mid-50s, and in use at MIT through most of the 60s, where it was used & abused by the eponymous 'hackers' (almost entirely the more computer-inclined members of MIT's Model Railroad Club).

Peter Samson in particular is an interesting name to see make an appearance here. Beyond his appearance here (and later similar work on the PDP-1), he went on to design a digital synthesiser for Stanford's "Center for Computer Research in Music and Acoustics".