As your part, say, “Dropkick me, Jesus, through the goalpost of life.” Odds are you won’t be asked to participate again.
I understand how you might want to appease them in the interest of peace at the dinner table, but true friends would not find it rude. They’d find it absolutely appropriate. They like you for who you are.
Matthew 6 is how I convinced an evangilical friend to stop asking me if I’d like to go to services. I’m a believer, but I don’t participate in organized religion.
I hate to say it, but depending on the sorts of personalities the friends’ friends have, asking to be skipped over while doing the blessing might lead to even more discomfort. Although the friend is probably going to be respectful of the OP’s lack of belief, it doesn’t mean his friends will be. I can just picture something like this happening:
The blessing is given and iamthewalrus(:3= smiles and looks away, or somehow else indicates he’s not playing, so he’s skipped. And then, once the blessing is over, the questions start. “iamthewalrus(:3=, why didn’t you say something? Aren’t you grateful for God’s bounty?” “You’re not a non-believer, are you?” Yeah, that’d be no fun.
Personally, were I in iamthewalrus(:3='s shoes, I’d hope that my host would be reasonable enough to change formats for the blessing. Like perhaps have one volunteer do it, or to take it upon himself to do it. I’m not sure how it’s different, just that it is, but in my family we talk about what we’re each grateful for at Thanksgiving, and it doesn’t have an air of prayer about it. Maybe it’s because our audience is each other, and God is just able to listen in if he likes; he’s not addressed.
I used to worry about that kind of thing, but I don’t with this friend (and his friends) anymore. I’ve certainly heard horror stories about overly pushy believers. But the most pointed question I’ve ever gotten from this social circle was, at a gathering shortly after I’d moved to Santa Barbara, someone asked me if I’d found a church yet. When I responded that I didn’t go to church, since I wasn’t religious, she said “Oh,” and changed the topic.
Until now, I’ve refrained from passing when my turn to speak comes because I felt like the discontinuity would bring attention to me at an inoportune time. I still feel this way. Hopefully, my friend will decide to change the format of the blessing, but if not, I’ll continue to give nondescript thanks, or to thank him for preparing the meal.
How about simply smiling, nodding, and looking at the person next to you for a pass? That way, you could acknowledge you’ve been given a turn but are choosing not to take it while not disrupting the ritual itself.
I too am an atheist, but I consider it good manners to partake in any grace or blessings that are being held in my presence. If the host requested that you get up and do a cheer for our footy/hockey/baseball team before eating, would you feel so personally offended by that? Or is it just the god stuff that has pressed your buttons?
Y’see, because I am a non-believer in any deity of whatever kind, it doesn’t bloody matter what I say…it certainly doesn’t make me uncomfortable, because I am not ‘betraying’ any actual belief by thanking my hosts’ deity, however they see him/her/it. Atheism is NOT a tenet per se, and we are not betraying our precious atheism by sharing in a prayer. It doesn’t hurt us to pray because our prayer is totally irrelevant. So is cheering on our football team when you come to think of it, but few of us would be ‘offended’ by that eh?
Well, I’d hardly equate a football cheer with acknowleging the existence of a god through prayer/verbal offering. However, yes…I find it weird when anyone gets offended if I don’t participate in ritual; whether it’s a cheer, a prayer, funeral stuff…whatever.
Well to me, saying it without believing it is not only disingenuous but it also mocks the believers. “Ok…suuuuuuure…‘Thank you for the turkey…blah, blah, blah…what a lovely gift you’ve given us.’” Kind of an Eddie Haskell response to something they take seriously. I see nothing wrong with being yourself among friends.
Are you ever going to share? Pins. Needles. Bated breath.
Will anyone be there you don’t like? Then this will do:
“Thou preparest a table before me in the presence of mine enemy.”
Beatle’s lyrics are often a good substitute:
“And when the night is cloudy
There is still a light that shines on me.
Shine until tomorrow
Let it be.”
You can get more mysterious if you want to:
“Blackbird singing in the dead of night,
Take these broken wings and learn to fly.”
or
“Picture yourself in a boat on a river
With tangerine trees and marmalade skies.”
No, they don’t make sense, but neither does praying to a god you don’t believe in.
I would tell my hostess and ask for her suggestion for a way out of it. You can always say “Check” or “By me” if she insists.
My brother-in-law gets caught in this same situation time after time by my mother and he is very natural about saying that he doesn’t pray.
I suppose it would be right out for you to stand up, pat your belly, and shout, “Rub-a-dub-dub, thanks for the grub, yay God!”
How about “it’s times like these when I just have to say thank god I’m an atheist!” 
That’ll keep 'em guessing…
I get in this situation at my parents’ house. Just ask your friend to seat you to his immediate right, and ask him to start the ‘round’. That way you’ll be last, and you can just say “Aaaa-men”. They’ll just figure that everybody already said the stuff you were going to say.
Actually I like the strategy you use now. Just mutter something about being thankful for the food and friends, no reason to invoke god.
What are you required to say?
The expectation is that I’ll say something. I don’t think there’s any social requirement beyond that and being polite.
And if you add in the fact that he has a rubber crutch, it makes the day complete. 
I suppose all you need to say is, “Thank you for inviting me into your home.”
Many people at Thanksgiving have a “Let us all say what we are thankful for” and I don’t see any problem with that.
As long as you don’t have to invoke Jesus or Alla or whatever, I don’t think I would have a problem.
If it is that big of a deal to you, you can host the dinner yourself, and not say grace, or you can stay away, or you can talk to your friend.
As I said before, it didn’t bother me when it was Thanksgiving because it wasn’t presented as a prayer. Later, for other dinners, it was more explicitly phrased as being a participatory blessing, which I am uncomfortable with.