I am a capricorn women and have dated libra men but it's never worked out long term. I think this is going to depend on your moon signs, rising signs, and positions of venus and mars, however. That said, my experience with this match follows:
On their own, cappie and libra aren't typically a good mix - cappie is determined and goal oriented. Libra is just trying to keep it's head above water and doesn't like feathers ruffled, confrontation, hard work, etc.. She is too serious for him and also too cautious. He doesn't get that she has a great sense of humor because it is dry and because she's seeing whether or not she can trust him before she really lets her guard down.
He mistakes her caution for coldness or snobbery (mistakenly of course!). His bruised ego may lead him to ignore her or worse - to insult her. Cappie likes to be pursued so she wonders why he takes so long to call. Probably, because he is a libra and doesn't know what he wants or what to think of her! She will have a hard time forgiving the affront. Next time she sees him, she will surely let him know how he wronged her. Libra man will think he was right about her.
Bye bye goes cute libra man. They are cute too, often with dimples and all. Damnit! Never worked for me. I wish you better luck than I have had!