If you haven't transferred the title of the vehicle to your name you can let your insurance agent know that you are planning to buy a car and can ask them if the insurance you have now will cover the vehicle until you have the title in your name. You could also ask them if they can place the car on the policy so that it's safe to drive it away from the purchase site. You will need to give Your insurance company more information after you have bought the vehicle.
If you are making payments on a car from family or a friend and they are holding the title until they are paid off then you might be able to find insurance but it will be harder to since you do not have the vehicle title. You could always contact your local Department of Motor Vehicles (DMV) to see if they are able to give you the information you are looking for.