"Could be" vs "Could have been"

The correct way to write is

It could have rained yesterday

or

It could have been raining yesterday

It should be :

It could be raining yesterday

or

It could have been rained yesterday

Either way, the word "raining/rained" depends on your previous word. If the previous word is has/have, it needs to be a past tense of the root word which is "rained". Similarly, if the word is "be" before the action words, then you should add a "-ing" behind.

Example :

I could be sleeping.

I could have been slept.

You can refer here :

https://www.really-learn-english.com/whats-the-difference-between-could-have-and-could-have-been.html

It may be learned in a proper order, like,

It could rain; It could be raining; It could have rained; and It could have been raining. It follows the order of say, It will rain; It will be raining; It will have rained; and It will have been raining; similar to future indefinite; future continuous, future perfect and future perfect continuous.

This order will help systematic study of other sentence forms. Example,

It will rain; Will it rain? Yes, it will; No, it will not (won't); Will it not (Won't it...?) When will it rain?

It will be raining; Will it be raining? Yes, it will be raining; No, it will not be raining; Will it not be (Won't it be...?); When will it be raining?

It will have rained; Will it have rained? Yes, it will have...; No it won't have...; Will it not have (Won't it have...?) When will it have rained?

I twill have been raining; Will it have been raining? Yes, it will have been raining; No it will not have been(won't have been) raining; Won't it have been raining? Why won't it have been raining?