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In Heinlein's 1966 classic "The Moon is a Harsh Mistress" the loss of self awareness in Mike (HOLMES) the computer struck me indelibly in my formative years. This speaks to Robert A Heinlein's tremendous abilities to develop his characters.

I can't think of a better example of a human created computer become conscious that was 'likable'. Hal was most definitely not likable in "2001: A Space Odyssey" and that film was from the same era.

What was the earliest appearance in SF of a likeable AI character? I'd like to read that book.

1939: Adam Link, the protagonist of "I, Robot", a short story by "Eando Binder" (Earl and Otto Binder); first published in Amazing Stories, January 1939, available at the Internet Archive; reprinted in Amazing Stories, April 1961, also available at the Intenet Archive.

From Wikipedia:

"I, Robot" is a science fiction short story by Eando Binder (nom de plume for Earl and Otto Binder), part of a series about a robot named Adam Link. It was published in the January 1939 issue of Amazing Stories, well before the related and better-known book I, Robot (1950), a collection of short stories, by Isaac Asimov. Asimov was heavily influenced by the Binder short story.

The story is about a robot's confession. Some weeks earlier, its builder, Dr. Charles Link, built it in the basement. Link teaches his robot to walk, talk and behave civilly. Link's housekeeper sees the robot just enough to be horrified by it, but his dog is totally loyal to it. The robot is fully educated in a few weeks, Link then names it Adam Link, and it professes a desire to serve any human master who will have it. Soon afterwards, a heavy object falls on Dr. Link by accident and kills him. His housekeeper instantly assumes that the robot has murdered Dr. Link, and calls in armed men to hunt it down and destroy it. They do not succeed; in fact, they provoke the robot to retaliate, both by refusing to listen to it and by accidentally killing Dr. Link's dog. Back at the house, the robot finds a copy of Frankenstein, which Dr. Link had carefully hidden from the robot, and finally somewhat understands the prejudice against it. In the end the robot decides that it simply is not worth killing several people just to get a hearing, writes its confession, and prepares to turn itself off.

Binder's story was very innovative for its time, one of the first robot stories to break away from the Frankenstein clichés.

Helen O'Loy by Lester del Rey was published in Astounding in 1938, the year before Eando Binder's "I, Robot".

Two young men build a robot intended for household duties, but end up with a sentient and beautiful female robot that falls in love with one of them. They marry, keeping Helen's robot identity a secret, and when her husband dies of old age, she begs the other guy to dissolve her.

Another possible answer predating this by more than three decades is the mechanical man Tik-Tok from Frank L.Baum's Oz books, first appearing in Ozma of Oz (1907).

Tik-Tok is a round-bodied mechanical man that runs on wound-up springs that must regularly be rewound. He is friendly and helps Dorothy out a lot. However, Baum has stated that Tik-Tok is not alive and cannot feel emotions. He is, however, a truthful and loyal servant. Not being truly sentient may disqualify him as an AI, although he certainly is likeable.