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.
You are First Cousins
They are cousins.
dappy and tulisa are cousins
You are cousins
Cousins
they would be cousins.
First cousins
They are cousins.
You are second cousins
Second Cousins