First one but there might be a better way to phrase it so that you have it in a less clumsy fashion - what is the context here? Is this a title under which you are asking people to list songs that help them sleep or something else?
Either is OK as the sentence is a defining relative clause. If the sentence was a non-defining clause (such as "songs, which help me sleep, are relaxing") then you couldn't use 'that'.
In everyday speech we would tend to use 'that' more, and in written text 'which' is more acceptable. But either is OK.
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