Can I park in a private parking spot if I know the owner won’t be coming in that day. Street parking costs money and I know that the man’s business is closed for the secular new year.
If there is no sign prohibiting parking in the private spot, it is permitted to do so. If a sign prohibits parking there, it is not permitted to park there.
This is a quite classic case of zeh neheneh ve-zeh lo chaser.
The owner of the parking spot is no losing anything by your parking there, while you are clearly benefiting from the vacant spot.
In halachah it is permitted to derive benefit from somebody’s property, and there is no obligation to pay him for the use, if we can assume that he permits the use (see Bava Metzia 117b; the dispute between the Sages and Rabbi Yehuda concerning using somebody’s property relates directly to the question of zeh neheneh ve-zeh lo chaser).
The Rema (Choshen Mishpat 363:6) writes that a person retains the right to forbid a person from using his property. Although it is possible that this right does not apply where a person cannot make any use of the relevant property (which may be the case for a vacant parking spot, which cannot be rented out; see Pischei Teshuvah 3), Poskim generally agree that even in this case we cannot force a person’s consent, and if he forbids the use of his property it will not be permitted to use it.
Therefore, if there is no sign forbidding parking (which is common), it can be assumed that the owner is not makpid, and it is permitted to use the spot. However, if there is a sign prohibiting parking, one cannot use it.