Sure. I have two first cousins once removed (i.e., offspring of various first cousins) who share my first name. At family get-togethers they call one another 'Cousin Skald" (and me “Uncle Skald”) to avoid ambiguity.
Also, my adult cousins and I use “Cousin X” to irritate one another all the time, as it sa circuitous way of calling the other person ‘country’ – a big insult in the Rhymer clan.
the cousins that are older than me are cousin x or cousin y. they aren’t my aunt or uncle but it seems undignified to just call them by first name.
I never addressed my cousins as “Cousin ____”, but when I was a kid my aunts and uncles were always “Auntie ____” and “Uncle ____”. When I got older “Auntie” became “Aunt”, and now as an adult I simply address my aunts by their names without the title (I only have one uncle left, and he’s only related by marriage - he’s always just been “Mike”). I’ll often use “Aunt ____” when I first greet greet them (I don’t see them often) but I drop the “Aunt” after the initial greeting. It’s similar to the situation I had with a high school teacher who was only six years older than me - while I was still in school he was “Mr. Teacher”; several years later I ran into him when my church softball team was playing against his, and I asked, “Hey, since I’ve been out of school for a while and you’re only six years older than me, is it all right if I just call you Scott?” And he thought that was fine.
The addressing situation I’ve always wondered about is parents addressing their son as “Son” instead of by his name. I’ve never heard this anywhere in real life - only in commercials, TV shows, and movies. And even on TV and in movies, I’ve never heard somebody address a daughter as “Daughter” instead of her name. The only time I’ve heard “Daughter” used as a form of address has been as an honorific or term of affection/authority, such as a a high priest or priestess calling a female acolyte or petitioner “Daughter”.
I call all of them “Cousin _______.”