"I have only had the car for eight days."
Translation:Mám to auto jen osm dnů.
Present perfect is more present tense than past tense. So the sentence "Mám to auto jen osm dnů" is perfectly correct. The sentence "Měl jsem to auto jen osm dnů" would be, in my opinion, "I had that car only for eight days" or "I had had that car only for eight days (before I ever learned to drive it)".
That would be used in the past. You crashed the car, so you have it no more, and you would complain "Měla jsem (to) auto jen osm dnů" "I had the car only for eight days." Or maybe you still have it but you are talking about a situation in the past "I had only had the car for eight days (when...)".