What I've usually seen is in those cases is the person being II instead of Jr. For example, my youngest son was named after his grandfather. He wasn't a Jr. but was a II. I've always just seen Sr. and Jr. used for fathers and sons, not any other way. There's no reason to give a suffix to a cousin named after someone because they aren't in each other's direct line, just share a common name. My eldest son is III because his dad is a Jr.. and his grandfather was Sr. So I'm fairly familiar on a personal level as well as from years of genealogy research on how the suffixes are generally used to provide clarity to the connections rather than confusion.
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