TIMATIC, via United Airlines, says that passports must be valid on arrival, but notes that there is a "Travel Certificate."
The Ghanaian embassy in Washington has a page on travel certificates that also notes that emergency passport extensions are available free of charge (I did not see where one might find the amount of the fee for a travel certificate application):
EMERGENCY TRAVEL CERTIFICATE
The Embassy of Ghana, USA, only issues Emergency Travel Certificate to Ghanaian citizens who for one reason or another are not in possession of Ghana passports and have to travel in emergency situations.
Applicants will be required to complete;
- Emergency Travel Certificate Forms
- Provide evidence of Ghanaian Nationality such as birth certificate or a photocopy of previous passport
- 2 passport size photograph
- Processing Fee
Applicants will be required to undergo an in-person interview at the time of submission of the Emergency Travel Certificate request.
Please Note: Emergency Travel Certificate are valid for only three months and does not replace a passport. Only applicants with real emergency situations will be considered.
[emphasis in original]
Our Embassy currently offers free Passport Extensions for persons who are unable to be physically present for the Biometric services required for passport renewals, due to unforeseen circumstances.
Applicants who wish to extend the validity of their passports are advised to send an email to [email protected] with the subject; Passport Extension and provide a detailed explanation of why an extension is needed.
Upon approval by the Consular Department, applicants will be contacted with specific instructions on how to proceed which will include applicants mailing their passports to the Embassy with a formal note requesting for Passport Extension. Applicants are strongly advised to include a pre-paid self-addressed Return Envelope.
Maximum Extension: 1 Year
Eligibility: This service is strictly provided on an emergency basis only. For example: Applicants who need valid passports for time-bound jobs or to renew their immigration status.
Finally, from https://www.traveldoc.aero/, a word of caution for Ghanaian citizens with multiple nationality:
Passengers who are dual nationals of Ghana are required hold a Certificate of Dual Citizenship issued by Ghana. These passengers must not enter and depart Ghana using different passports.