Can my dad co-sign if we’re both US citizens and I don’t have any income?

Although not completely clear from your question, I presume that you are a U.S. citizen; that your husband is in the United States after having entered legally and with inspection; that your own documentable income is insufficient to satisfy the legal requirements; and that your father has sufficient documentable income and he is willing to be a joint sponsor of your husband. If that is correct, then your father would need to provide a signed Affidavit of Support form with acceptable documentary evidence about his recent and current income. He then would have the obligations that are specified on the Affidavit of Support form. Note: you, as the primary sponsor of your husband, also would need to file a completed Affidavit of Support form, even if you currently have no income. The application process for a marriage-based adjustment of status case can be more complex than it initially appears, and errors in completing the forms or failures to provide complete sets of required documentary evidence can cause substantial delays or even more harsh consequences. It would be wise for you and your husband (and, perhaps, your father) to consult with an immigration attorney who then would be able to advise about eligibilities, options and strategies and would be able to provide legal representation in the application process. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

Your dad can sign I 864 or I 864A depending on your living situation.