I want to know if someone with a Temporary green card residency status can sponsor an immigrant petition. My cousin from Ghana is married to a US citizen and both of them are not working presently, Can i sponsor the marriage application even though I have a Temporary green card Status.
You seem to be asking if you can sign an affidavit of support as a "joint sponsor" and if you are a conditional, lawful permanent resident, you can.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
I think you mean can you sign the affidavit of support. Yes you can if you earn sufficient income.
If you mean can you sign their I-864 Affidavit of Support, yes. Be aware, however, that by doing so, you assume some financial risk that your cousin's spouse will need government assistance when s/he comes to the U.S.
You should always consult with an experienced immigration attorney to make certain that the advice you received is appropriate for your particular immigration case.