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Ah, I have an exellent suggestion for this case:
Я буду любить тебя до (самого) рассвета.

This usage of "любить" is kind of old-fashioned, I think.
When at a wedding party somebody says "любите...

I think that the way the expression "заниматься любовью" is used, it's just a euphemism for "заниматься сексом".
Which begs the question: how much different the expressions "have sex" and "make...