Just ASK your cousin what would be appropriate, rather than guessing. There’s no reason not to ask. As others have said, standards differ and concepts of ‘formal’ differ. You won’t appear ignorant, you’ll only appear concerned about doing the right thing for her wedding. Probably it simply means jacket and tie.
If you’re concerned enough about sticking out, to ask on a forum, I concur that you should ask.
In my experience, the modern interpretation for dress standards are:
Semi-formal - suit no tie permitted, If you’re pushing it maybe slacks & a sports coat
Formal - Suit with tie (used to mean a tux, but has fallen by the wayside IMO)
Black Tie - Tux
However different people interpret these differently, in particular depending upon the age of the person doing the invites. Formal could easily mean a tux, but I suspect you’d look out of place.
A tux is inappropriate because you may be out dressing the groom and ushers. A tux is a step too far. Formal does not mean me tuxedos. Black tie and white tie mean tuxedos for all. Formal means fancy but not tuxedo fancy!
Wear a dark suit and tie as others have recommended!
A tuxedo is inappropriate because it’s a day wedding. You should wear morning dress!
Serious question: Since the reception is in the evening, should you change clothes for the reception or is a morning coat still appropriate?
And if you do change, what should you wear?
Lighter suit for the afternoon ceremony. Darker suit for the evening reception.
If you don’t want to have to get two suits, wear the dark suit to both but have a lighter (or more colourful tie if that’s your thing) for the ceremony with a more casual white shirt perhaps with button down collar (use a half windsor knot for the tie). For the evening, a dark, more monochromatic tie, simple tie bar if you like, and a more formal white shirt, one with a spread collar and perhaps french cuffs and cuff links (use a full windsor knot for the tie).
This is why Betazoids have nude weddings.
Because they don’t know how to tie a windsor knot?
One would never wear a morning coat in the evening, but instead would change into white tie.
You should change. In this modern age, a tuxedo’s OK for that. White tie is a bit much…
Reception is at 6PM. Is that Evening, or still Afternoon?
Evening. Unless it ends at 8pm.
OP said something about “fancy lounge”. Not sure if that means hors d’oeuvres and drinks only, or if it’s followed by a sit down dinner.
If the former, you can loose the tie altogether but still go with the dark suit and the more formal white shirt.
Without reading the other comments, I’d say you’d be safe to dress one notch more formal than “Sunday church attire”…whatever that means for the bride and groom, at least.