This issue has been discussed so many times.
As a GC holder, your cousin unfortunately can not do anything to bring spouse.
Her husband has to come to the US on his own with his own status.
The best visa is her husband gets H1 or L1 visa which allows dual intent
so that there is no issue to obtain it even though wife is GC holder living in the US.
Another option is getting F1 or B visa, but these visas are likely to be denied at
consulate because wife is living in the US with GC, and it raises suspicion of immigration intent.
