"...Can I use other oils with the pine tar like olive oil or coconut oil? ..."
Pine tar is an additive to a soap recipe. It doesn't take the place of regular soaping oils -- you'd end up with a gloppy mess!
Pine tar does use a tiny bit of lye, so you do need to include it as part of your oils when calculating the water and lye needed for your soap recipe.
The easiest way to make a pine tar recipe is to use your favorite "regular" soap recipe with your usual superfat % -- just add whatever additional weight of pine tar to it that you want to use. (I used 10% pine tar by weight of oils.) Enter the weights of the oils and pine tar into soapcalc to get the lye and water needed. This method will increase the total amount of soap batter a bit, so use a mold (or molds) that can handle a little more soap batter.
If you need to control the total volume, then use your regular soap recipe but scale the weights of the oils down down until the total weight of the pine tar plus your regular oils is equal to the total weight of oils you normally use. Enter the revised oil and pine tar weights into your
soap calculator to get the lye and water needed for the pine tar recipe.
I used 10% pine tar based on oil weight, but the range can be from 5% to 20% or even more. The more pine tar, the softer the bar, especially at first. Mine were a bit soft at first, but have hardened up nicely in 8 weeks. From what I've read about others who are more adventurous than me, the pine tar can cause the soap to stay very soft if you use 20% or more.
I hope that helps!