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My new books, which have black covers, are on the table.
I read that this was a non-defining relative clause but I think it is a defining clause because if there are many books on the table how do I know which books are new if I don't have the essential information of the black covers?
Your example is a non-defining clause.
Non-defining clauses are usually introduced with "which", and could be removed without changing the meaning of the sentence, for example:
My new books are on the table.
This is a complete statement. The fact the books have black covers is not particularly relevant. In fact, in your original example, the clause in question is even placed between parenthetical commas indicating that this information is not wholly necessary. It could have been written as:
My new books (which have black covers) are on the table.
If the fact the books had black covers was important, perhaps to distinguish them from some other books, then you would make it a defining clause, usually introduced with 'that', for example:
The books that have black covers are on the table.
