A couple suggestions:
My little brother's bday is right near Thanksgiving. My moms is middle of August. A few years when we were kids, she swapped birthdays with him so he could have not only a party not near a holiday, but one in the summer as well. For his proper birthday, we'd then have a cake and candles but no real party.
My cousin was born on Christmas Eve as well and my Aunt and Uncle used to let him have his birthday party at his 1/2 year. This allowed the party with friends away from the holiday. On Christmas Eve, she does still have a small family dinner with just a few presents (NEVER wrapped in Christmas wrap-always with birthday paper so he doesn't feel like it was really a christmas present being 'regifted').
My twins were born on Halloween!! We lucked out as far as holiday birthdays go, since we get to use it as a theme if we want or just have the party on the weekend. The cool thing is that they love that people give them candy on their birthday!!