There is no legal prohibition against using a co-sponsor to support a K1 Fiance Visa. Whether it will be accepted or not by the US Embassy to support the fiance visa application is the issue.
It has been determined that the I-134 Affidavit of Support, unlike the I-864 Affidavit of Support used for Marriage Visas and Permanent Residency applications cannot be lawfully enforced due to the non-immigrant nature of a K visa. Nevertheless, most US Embassies around the world will give some consideration to a co sponsor’s willingness to help support the financial requirements of a Fiance Visa. The good news is most US Embassy’s will accept a Co-Sponsor and those that frown on it will likely give it some consideration depending on the facts of your case.
One reason for accepting a co-sponsor for a K visa applicant may be the recognition that a co-sponsor will be accepted if the parties were married and applying for a Marriage Visa or Legal Permanent Residency. It seems almost silly to exclude the use of a co-sponsor for a K visa when the parties intend to marry and subsequently apply for Legal Permanent Residency, at which time a co-sponsor can be used. Another reason for possibly accepting a co-sponsor for a K visa application is to try and help the US citizen marry his or her choice of a loved one.