Amy,
I've so been there with difficult child 1. More than once she sat here in her party dress in tears because no one showed up. Not even some family members. It broke my heart. We didn't have any other options or social contacts for her other than school & our neighborhood.
Our solution was to make her birthday a family adventure day. It would start with a mother-daughter lunch, just the two of us, wherever she wanted to go. (I would pick her up from school with balloons, whistles, anything to make it all a big deal in front of her classmates - with the teacher's okay beforehand. It made her feel special when the kids would say "I wish MY mom would come get ME like that on MY birthday...") Then, depending on whether it was a schoolday or not, we'd go to dinner and a movie, or to a "big rat" type place, whatever she wanted to do. Then we split up visiting her relatives on different days with different events, so that her "birthday" stretched over an entire week. By the end of the week, she'd had 2 or 3 different birthday cakes, got to see all her favorite relatives, been on some "neat" adventure or other, got to see a movie she wanted, plus got lots of presents. That week would be so jammed-packed with birthday events, she barely noticed her own lack of friends. We never let her have that opportunity to "see" everyone in one room and realize her serious lack of numbers.
Now, she's a little older, a little better at making and keeping friends, and we can actually have birthday parties for her. This past Saturday, as a matter of fact, was her 14th birthday. We had a cook out. Several folks didn't show, but that was actually a good thing because she still wound up with 11 kids and 5 adults at her party. She had a blast. All the kids had fun. (Mom actually let her turn up the music without complaining - even though I think my ears are still ringing. lol) It was a real treat to see her having a "normal" young girl-type experience.