Sometimes, you might be willing to give a fired employee a positive reference. After all, an employee who wasn't a good fit at your business might do well elsewhere. If you can say positive things about the employee, then say them.
If, however, you are not comfortable giving a positive reference, then you shouldn't. In such a situation, less is better than more.
When prospective construction employers call, tell them that you can only confirm dates of employment and job responsibilities and no more. You must take care not to bad mouth the employee to a prospective construction employer, because this will leave you vulnerable to a defamation suit from the former employee. It will also reflect poorly on your construction employer. You can always use the comment ?Mr/Mrs. _ is not eligible for rehire with this firm?. This will certainly get the point across to the prospective construction employer.