Do Catholic Churches marry on a Sunday?

Not to my knowledge. Depends on the priest and diocese. Every one is different so it's hard answeing.

Generally no, but you should talk to your priest.

As these other ladies just said, some do and some don't, so you'll just have to check locally. I've been to a Catholic wedding on a Sunday previously, so I know it's possible.

Exactly...check with the parish. The church I'm getting married in specifically said no Sunday weddings.

Usually you have to work around their mass schedule so it is going to depend on the specific church. I would just ask them directly.

Contact the church. Depends on the priest