LOS ANGELES (AP) _ Michael Dukakis' finger-jabbing sternness was gone and George Bush's syntax was uncharacteristically ungarbled.

What the American viewers saw instead were two fellows who say they are optimistic about their country, know the sorrow of losing a child and are committed to certain basic values of American life.

Occasionally, these rivals even acted nice to one another. They appeared eager to be courteous, each holding up a hand for silence when their supporters booed or clapped contrary to the pre-debate entreaties of the organizers.

Both candidates went into their second face-to-face debate with an avowed goal to show how personable they could be.

Bush said his goal was to show people his heartbeat. Dukakis adviser Rep. Tony Coelho, D-Calif., said his candidate had to undertake ''a conversation with the American people.''

From the start of Thursday night's presidential debate on the UCLA campus, the two candidates appeared to be making that effort - Bush demonstrating how relaxed he was and Dukakis looking for ways to show that he cared about people.

In the affability category, both candidates made strides over their performances in last month's first debate in North Carolina. Dukakis, often accused of being grim and robotic, smiled a lot. He used gestures that were more expansive than his trademark jabbing thumb.

Bush mangled his sentences less often than usual.

He smiled easily and often, showing an ''aw shucks'' attitude. He clearly took the honors in folksiness.

Asked about the so-called sleaze factor in the Reagan administration and whether he would work to ban people from lobbying government agencies they once worked in, Bush said he would.

Then, cocking his head and smiling as if telling a secret, he added, ''You see, I am one who - I get kidded by being a little old fashioned on these things - but I do believe in public service.''

The debate was short on the kind of slashing one-liners that characterized the North Carolina faceoff. The zingers were still there, but they were repackaged and delivered with a smile.

When the issue of abortion came up, both took advantage of opportunities to reveal themselves by talking about their children who had died. Bush, who rarely discusses the leukemia death of his young daughter, Robin, told matter- of-factly how he learned the news.

''The doctor said, beautiful child, your child has a few weeks to live,'' he said. After her parents took her to a New York specialist, ''the child stayed alive for six months and then died.''

Dukakis said, ''Kitty and I had very much the same kind of experience the Bushes had: we lost a baby, lived about 20 minutes after it was born.''

But Dukakis went on to say it should be the mother's choice whether to abort.

Dukakis answered without visible emotion when asked whether he would favor the death penalty should his wife be raped and murdered. He responded negatively, passing over the chance to personalize the answer or mention his wife.

And Bush, in response to a question about whether he could think of anything good to say about his rival, complimented Dukakis for his pride in his family and Greek heritage.

Dukakis, in reply, managed to get in a dig about Bush's favorite label for him, saying that Bush, for once, hadn't used ''the word liberal or left one time. ''I thank you for that,'' he said.

He went on to say that there are ''things which all of us believe in. We may have different approaches. We may think that you deal with them in different ways. But they're basically American. I believe in them; George Bush believes in them.''