Love first, both of them
Cancer and Libra both put relationships at the heart of everything, and they don’t apologize for that. Libra can create an atmosphere: flowers, music, a thoughtful question at just the right moment. Cancer can make a home you never want to leave. Each knows how to be considerate, and they’re often very tender in the early days.
They bring out something different in each other, too. Libra gets a Cancer to put on nice clothes and go out and meet people. Cancer shows Libra what it’s like to be loved without having to be charming every minute, and that can be a big thing for someone who’s been pleasing people since childhood.
Politely not fighting
Both are cardinal signs that start things, but they begin from different places. Cancer goes by feeling, and Libra goes by what seems fair and reasonable. So when Cancer’s upset, Libra may offer a balanced view of both sides. That’s a very bad idea. “I can see why your mother said that” is seldom what a Cancer wants to hear. Libra, meanwhile, can feel overwhelmed by the strength of a Cancer’s mood, and may look for an excuse to step outside.
Neither likes direct conflict, so tension goes underground. Cancer hints and sulks. Libra stays pleasant and spends more time with friends. It’s all very civilised, and neither one is getting what they want.
An honest row now and then
You’re allowed to disagree. Try scheduling it, if that’s easier: “Can we talk about your mother after dinner on Thursday?” Libra can start by taking Cancer’s side for a full minute, before offering any balance at all. Cancer can name what they want and not just what’s gone wrong. Then hug. Neither sign has to give up being kind.
A square between Suns is a modest thing, as these contacts go. How you actually comfort each other is a job for the Moon and Venus, so look there before deciding how well this might work.