"If I knew you're coming I wouldn't have come"

Is the statement

If I knew you're coming I wouldn't have come

correct? Should we use

If I had known you're coming, I wouldn't have come

instead? Please consider American-British differences.

What is required here is the Third Conditional, in which the speaker imagines a situation which hasn’t actually happened. In this example, the speaker didn’t know the person addressed was coming, and so, we are led to believe, the speaker came as well. The usual form taken by the Third Conditional is if + past tense of have + past participle of the main verb, followed in the main clause by would have + the past participle of the second main verb. This produces If I had known you were coming, I wouldn't have come. A simpler example is If you had run, you would have caught the train.

The past tense may sometimes occur in the if clause (If I knew you were coming . . .), but in British English, at least, it would be unusual. That said, I expect some of us will know the song that has the line If I knew you were coming, I’d have baked a cake.

A standard way to say this in the US is

If I'd known you were coming, I wouldn't have come.

You cannot contract "you were" to "you're"; this contraction is reserved for "you are". However, "I had" can be contracted to "I'd", and I suspect it usually would be in speech.