Does this person avoid all sugers, or just processed ones? You could make a fruit salad?
Or the Banana One ingredient Icecream?

Ambrosia, modern style--lots of delicious citrus fruit cut up with toasted, unsweetened coconut on top (if you can guarantee it's gluten-free).

Or you could do a big gluten-free cheese (there are plenty of options) and fruit tray.

Britt, there are some delicious fruit tart recipes that are both (processed) sugar and gluten free. You could make one big one or individual tarts for each guest.

There is a blog I think called Elana's Pantry that this website has quoted from before, I think they posted her Strawberry Muffin/Cupcake recipe. Anyway, she uses coconut flour and agave nectar in all of her recipes. Her cupcakes are moist and delicious and super easy to make, especially if you have never baked gluten free before. I don't know if your friend will eat agave nectar or not...but it's a nice option, and a lot of the cupcakes don't need an icing option.

There is a new book out with wonderful recipes: "A Sweet Life Without Sugar:
Naturally Sugar-Free & Gluten-Free Artisan Recipes" by Joan Miller. Available at http://www.be-well-now.com/sweet-life.html

if your friend will accept a sweetener like agave or honey in her cake, i'd recommend this lemon trickle mash cake. simply substitute the sugar for a sweetener of your choosing. it was a huge hit with my friend who never gets to have the "birthday cake" experience because of grain sensitivities.
http://www.channel4.com/4food/recipes/chefs/hugh-fearnley-whittingstall/tim-s-lemon-trickle-mash-cake-recipe

I'm gluten-free and always trying to suggest things for my inlaws to make for me. I'm not sugar-free though, but I'll try to help.
For Snacks:
-Homemade hummus with veggies and gluten-free crackers or corn chips
-Salsa and chips
-Roasted nuts with herbs
-Cream cheese and olives on celery (if they can do peanut butter, you could also do sugar free pb w/ raisins on celery)
For Sweets (this is way harder):
-If your co-worker does honey, you could bake some apples in a little water with honey and lemon juice
-Strawberries (or any other sweet fruit) and whipped cream (not sweetened)

http://www.alldayidreamaboutfood.com/2011/06/flourless-chocolate-torte-with.html

She does a lot of gluten free and sugar free/low carb recipes. I think this is your best free source =) good luck

Gluten free AND sugar free? I'm very of the mindset that for a birthday party, while the birthday girl should like what you make, its for others to enjoy too, and I'd bet everyone else is going to be pretty let down to find a "birthday party" full of gluten/sugar free things! That translates to me as cake for everyone else she can blow out and a nice fruit plate with some cheeses for her (I'm assuming the no sugar thing means no processed sugar, not fruit sugars. If not...just cheese? lol) Good luck! That kind of stuff is always tricky.

Is this a surprise party? If not, just ask her what she likes! My pet peeve is when people insist I eat Mexican because much of it is gluten free, even though I don't like Mexican food. Some ice creams may be sugar and gluten free. Be sure to read the ingredient label. Frozen bananas may go nice with something sweet like honey or sugar-free chocolate, if there is such a thing. But you may end up with artificial sweeteners.

Totally agree with Emmi! If you can, ask her what's acceptable and what's not. It REALLY sucks to feel "forced" to eat something you're not cool with, almost as much as it'd suck to have a birthday party filled with food you can't eat...in that case, it's better not to have a party at all.

You could do baked apples stuffed with walnuts, raisins and cinnamon. If unrefined sugars are OK, you could add maple syrup or agave on top.

Super easy tarts - take gluten free cookies in a plain flavor (gluten free sugar cookies, graham crackers, or animal crackers would be perfect) and crumble them up into cookie dust. Mix with melted butter & press into the bottom of a pie pan. Then fill with fruit and if unrefined sugars are OK, drizzle with honey. heat it up and serve the tart with gluten free ice cream (most ice creams do not have gluten ingredients, but always be sure to check the label).

There are also tons of recipes for gluten free pie crust that aren't too intimidating at all, so if you'd rather make a pie than a tart, that would also be lovely.

Anything with almond meal would be gluten-free, deliciously rich, and not too sweet.

Also, why not an egg custard sweetened with fruit and/or honey/maple syrup?

If you use a naturally sweet fruit like pears or dessert apples, you can make baked/roasted fruit or a fruit sauce without sugar or really any other kind of sweetener very easily.

Of course these are all dessert suggestions. For gluten free, you can't go wrong with a nice bean and meat chili and some gluten-free, sugar-free corn bread! I made some for a party (minus the gluten and sugar restrictions) a few days ago and it was a big hit! Made the chili in the crockpot and it was a cinch.

Roost (http://www.roostblog.com/) and ScandiFood (http://scandifoodie.blogspot.com) have plenty of sweet (including cakes) recipes that are gluten and sugar free (and mostly dairy free as well).

Erin McKenna from Babycakes has great birthday cakes and she came up with an amazing recipe book. You can bake muffins, cupcakes, cookies, etc... all gluten and sugar free (she uses agave nectar instead of sugar). Worth checking out.

@Greybeard - way to be the life of the party. Hope Karma doesn't decide to snap back at you like a fast rubberband...

http://tankitchen-dessert.blogspot.com/2009/02/coconut-rice-pancakes.html
I made these rice flour coconut mini cakes for a birthday party last weekend. They were an unexpected hit! I used my mini cupcake maker to cook them in. They're absolutely delicious!

I used to have a gluten-free sugar free flatmate. Her staple was buckwheat pancake, so maybe some blini with sour cream and salmon could be nice.

if you're looking for GF, sugar-free dessert, try searching a place like Mark's Daily Apple for "dessert." You can find something awesome like a decadent coconut chocolate mousse (http://www.marksdailyapple.com/decadent-coconut-milk-whipped-cream-with-berries-and-dark-chocolate-coconut-mousse/). There's plenty of awesome choices -- an easy way is to look for stuff under Primal or Paleo, as they tend to shy away from gluten as well as sugar.

Avoid adding things like agave, corn syrup, or honey, as they are all sugars. There are plenty of "regular" foods that don't have gluten or sugar in them -- just read the label. Sauerkraut, kimchi, yogurt, meats, bacon, sausage, coconut... You don't have to stick to just cheese!

You can have mega delicious desserts that are gluten free and you can sub agave for the sugar. Check out http://glutenfreegoddess.blogspot.com/. She has tons of ideas.

Strawberry Cannoli are a fav of mine: http://theworldaccordingtoeggface.blogspot.com/2009/06/strawberry-cannoli.html :)