There are two obstacles to overcome when planting grass under pine trees: the relatively little sun your grass will receive and the large amount of acid the trees add to the soil. Once you have overcome these two challenges you can grow luxuriant grass under any pine tree.
Rake up all pine needles and pieces of bark are under your pine trees. The more pine debris you can remove the better. Pine needles add a tremendous amount of acid to the soil under the tree, which kills most grasses.
Work up the soil under your pine trees with a garden tiller. This can be difficult, depending on how close to the surface the roots of the pine trees are. Use a shovel to break up and loosen the soil around roots where you cannot use the tiller.
Spread about 25 pounds of lime over a tilled circle with a diameter of 10 feet. Use more or less lime depending on the size of the area you need to cover. Wear a breathing mask whenever spreading lime.
Spread 10 pounds of organic fertilizer or starter fertilizer over the area.
Spread 3 pounds of shade-tolerant grass seed evenly over the area. Use a hard steel-tine rake to work the seeds into the soil and organic fertilizer. Only rake the top half-inch of soil/fertilizer.
Water liberally with a soft sprinkler. Make sure the water penetrates the top inch of soil. Sprinkle the area every day or two. Keep the top inch of soil damp but not muddy. Your seeds should sprout within a week to 14 days. Do not walk on the new grass for a minimum of 21 days following germination.
Keep pine needles raked on a regular basis. Spread lime once each growing season.