Clive Rees, from Tumble, was celebrating his 65th birthday on the Caribbean island with his wife Sonia when he was hit by a car.
He is being treated in an intensive care unit after developing pneumonia and breathing difficulties.
Mr Rees is unable to return home on a commercial flight and the family is raising money for an air ambulance.
They have made a heartfelt plea to the public to help them reach their target following the incident on 13 May.
"You always think something like this will never happen to you," said daughter Tracy Rees.
"We just want him home."
Miss Rees said the response has been "overwhelming", with support from family, friends and local businesses.
"We've raised about £2,000 so far," she said.
"I just can't believe how generous everyone is. Thank you from the bottom of our hearts."
The £65,000 air ambulance fee encompasses a return trip from the UK, refuelling and a team of medical staff to look after Mr Rees.
A family in Carmarthenshire must raise £65,000 to fly their injured father back from Barbados.