What is the common way to say "the rain reduced in intensity"?

Solution 1:

There are many idiomatic options:

• the rain eased off
• the rain let up
• the rain slackened off
• the rain eased up
• the rain tapered off

Google ngram showing relative usage

You can even replace "the rain" with "it", as long as its already clear from context that it's raining. Random examples:

As if to prove that the weather was definitely not on his side today, the rain grew heavier.

"The band stand's just around the corner. We could shelter there till it eases off. The weather report said 'A few showers'."

The Wishing Well by Anna Jacobs

and

"Sarge, got the base on the radio. They said that they expect a break in the weather at anytime. They'll have a chopper inbound as soon as it lets up."

Return To Hell: U.S. Marines In (Vietnam) by Charles F. David