not a teacher
1 "He has no intention for marriage."
2 "He has no intention of marriage."
3 "He has no purpose for marriage."
4 "He has no purpose of marriage."
I feel that none of these sentences is natural English, although #3 may convey the unlikely meaning: "He can not put marriage to any use".
For the meaning that I think you intend, common phrases would be, "He has no intention to marry", "He has no intention of getting married", "He has no intention of marrying".
ps: I keep thinking #2 might be ok, I'd be interested in another opinion.