I just sold my car privately. It really is going to depend on the demand for the vehicle, the condition it's in, and the price you set.
I had mine around 1000 below the Black book value shown on autotrader as it had a couple minor issues - and I sold it for asking price within a couple days with numerous inquiries - which was almost triple what the dealer would offer on trade. However I've also listed vehicles for months on end without any responses.
Anyway over the last few years I've listed 5 vehicles and sold 2. If you want yours to go quick advertise on any site you can (autotrader, kiiji, ebrandon, facebook marketplace, etc.) and be sure you are well below the price of other similar vehicles. If yours is either desireable, or in good shape you will still get more than you would on trade, but unless you have something really special (or a lot of luck) you won't sell it quick for a good price.
Quick or Good Price - pick one.