Unfortunately, no. As many of us are crime victims too, we can absolutely sympathize with your situation: both with your desire to get your property returned, as well as the strong motivation to see those responsible for this crime punished.
However, the tax code does not contain a provision for a cost of this kind, as money spent on or toward the recovery of personal property is not a tax deductible expense that the IRS recognizes. Instead, the law would classify the cost of hiring private detectives as a personal item -- unless the stolen car were used as a business vehicle of some kind, or in the production of taxable income. In that event, what you've paid to the private investigators could legitimately be deducted as a cost of doing business (i.e., a business expense).
The only idea to offer that might provide some kind of tax relief here is filing for a casualty & theft loss. You can read more about that particular tax deduction here:
https://ttlc.intuit.com/questions/1901178-casualty-and-theft-losses
https://www.irs.gov/taxtopics/tc515.html
Once again, we are sorry to hear that you've been a theft victim, and sincerely do hope that you eventually will recover your automobile.
