The Greek word for cousin is anepsios.
Cousin is used at least twice in Luke. Luke 1:36 and Luke 1:58 uses it and the Greek word here is Suggenes. Suggenes means kinsman, cousin, kinsfolk, and kin.
If the writer wanted to mention a “cousin,” most likely the word anepsios would be used. For another kinsfolk(or even as a cousin) the word “suggenes” would probably be used.
But Jesus had “brothers” and whether he had cousins or not is not related in Scripture. However if Mary had cousins, then Jesus would have had cousins as well. Example: If Mary and Elisabeth were first cousins, the Jesus and Elisabeth would be first cousins once removed.
Luke 1:36 - Elizabeth is Mary’s kinswoman. Some Bibles translate kinswoman as “cousin,” but this is an improper translation because in Hebrew and Aramaic, there is no word for “cousin.”
Luke 22:32 - Jesus tells Peter to strengthen his “brethren.” In this case, we clearly see Jesus using “brethren” to refer to the other apostles, not his biological brothers.
Acts 1:12-15 - the gathering of Jesus’ “brothers” amounts to about 120. That is a lot of “brothers.” Brother means kinsmen in Hebrew.
Acts 7:26; 11:1; 13:15,38; 15:3,23,32; 28:17,21 - these are some of many other examples where “brethren” does not mean blood relations.
Rom. 9:3 - Paul uses “brethren” and “kinsmen” interchangeably. “Brothers” of Jesus does not prove Mary had other children.
Gen. 11:26-28 - Lot is Abraham’s nephew (“anepsios”) / Gen. 13:8; 14:14,16 - Lot is still called Abraham’s brother (adelphos") . This proves that, although a Greek word for cousin is “anepsios,” Scripture also uses “adelphos” to describe a cousin.
Gen. 29:15 - Laban calls Jacob is “brother” even though Jacob is his nephew. Again, this proves that brother means kinsmen or cousin.
Deut. 23:7; 1 Chron. 15:5-18; Jer. 34:9; Neh. 5:7 -“brethren” means kinsmen. Hebrew and Aramaic have no word for “cousin.”
2 Sam. 1:26; 1 Kings 9:13, 20:32 - here we see that “brethren” can even be one who is unrelated (no bloodline), such as a friend.
2 Kings 10:13-14 - King Ahaziah’s 42 “brethren” were really his kinsmen.
1 Chron. 23:21-22 - Eleazar’s daughters married their “brethren” who were really their cousins.
Neh. 4:14; 5:1,5,8,10,14 - these are more examples of “brothers” meaning “cousins” or “kinsmen.”
Tobit 5:11 - Tobit asks Azarias to identify himself and his people, but still calls him “brother.”
Amos 1: 9 - brotherhood can also mean an ally (where there is no bloodline).