The relationship between you and your cousin's spouse is that of a cousin-in-law.
If it is not your common grandparent, there is no relationship.
Your cousin' spouse becomes your cousin by marriage (cousin-in-law). The reason for this is that they have the same relationship to you.
dappy and tulisa are cousins
Cousins
You are cousins
You are First Cousins
They are cousins.
First cousins
You are second cousins
They are cousins.
Second Cousins
First cousins