From the
YouTube channel BBL 80s 90s:
CHANNEL 4 BASKETBALL
Bolton Bees v Manchester Giants, 1983/1984
So, there certainly could have been other on-screen scoreboards before 1992

It makes sense that high-scoring basketball had them before football, but I didn't expect it to be British basketball...
From the same YouTube channel...
Here's BBC One carrying an on-screen scoreboard in
1991
. But maybe not one that they chose or wanted!
This was only used during "brief highlights" introduced by Steve Rider.
BBC Sportsnight - Kingston BC v FC Barcelona, 30.01.1991
The Genome entry for the show confirms that this was played the same night.
These graphics have a lot in common with Channel 4's previous ones. The scorebar is just a clock, team colours and scores without names. The graphic is main-camera only, not appearing on replays or the other cameras.
The graphics and camerawork don't look very "BBC" to me – the style and fonts, the replay wipes, even the crash-zoom when a shot hits the basket. It makes me wonder if the Beeb just purchased this coverage and someone else made it. But who? Maybe another broadcaster, maybe the organizers FIBA, maybe Kingston hired a production company? (It was held at Crystal Palace.)
The tournament is the European Champions Cup 1990/91 – details
here. Kingston were eliminated early, but Genome says BBC covered a few games including Barcelona above. We have extended video highlights of the match a week later, against Aris of Greece, apparently
added to Grandstand at short notice. This time, no continuous scoreboard. And lots of Greek supporters and Kevin Cadle getting very excited.
Kingston v Aris Thessaloniki, 07.02.1991, shown 09.02.1991
BBC TV had shown basketball
as early as 1949, and broadcast a lot of it
through the '80s. They rarely covered European club tournaments,
in 1985 and again in 1991 because Kingston made Europe's final 8. As an example of how they probably "preferred" their graphics to look, this is from their coverage of the national league
Sunderland v Thames Valley highlights (from Grandstand
13.04.1991). A few score updates, every couple of hours

You don't want to give people too much information.
Not on BBC, but from the final of that Euro Champions Cup tournament,
some
clips contain a scorebar - only the team colours and scores plus the FIBA logo.
Barcelona v Jugoplastika (KK Split), played 18.04.1991
No reason why FIBA couldn't have done that at the time, but I think this scoreboard was added years later, the way ESPN Classic does. It looks a bit too good for 1991, and doesn't fit with the other graphics on the game clips. And the VHS off-airs of the national TV coverage don't contain it.
There's an early (and remarkably low-quality) "score in the corner" in this clip from 1985. But again, it wasn't shown during most of the coverage. It's from the end of the basketball
Cup Winners' Cup final:
Barcelona v Zalgiris, 19.03.1985
They call a digital onscreen graphic a "
DOG"... So, if it's superimposed
Monty Python-style, is it an analogue graphic? An AOG?
This graphic isn't in
other clips from the game, because the director was too busy annoying everyone with the TVE logo.