If you can, can you tell me what type of grasses are available to you there, and what your conditions are temperature wise in the summer and winter, and also your rain fall.

As mentioned before the Pine trees are going to compete very heavily with any type of grass you put under it. I would like to suggest that you simply dont put any grass within 10-15' of the pine trees. I say this for a couple of reasons. One it can be harmful to the tree itself, as the grass will compete with the tree for nutrients, and water. Also there are studies that show trees do best with only mulch under their canopies. Also there are many pictures of golf courses showing a tree line, and from 15' away from that tree line where the grass is inside that 15' it is very weak.

Also constantly driving your mower over the roots can cause compaction and you can even cut roots that are on the surface. Both cases are bad for the trees.

So to save some possible trouble I would suggest mulching the tree base with their own pine needles, and forming a nice edge 10-15' around the trees.

If this is not possible due to the amount of trees you have and if you did this would make your lawn look like a bunch of circles with spots of sod, then I would need to know your conditions and grasses available to you. But I would still try to get some form of a buffer between trunk of the tree and the grass line.

Hope that helps.