If your neighbor/coworker/etc. is a religious non-Jew and they do you a favor, is there a problem to say "thank you, God bless you?", assuming you think they'd appreciate hearing that?
I can't imagine it would be a problem.
Hashem blessed Avraham "והיה ברכה", which Rashi explains as "Blessings are given into your hand". That implies that we have the power (and responsibility) to disburse brochos. We also have a responsibility to educate the nations of the world about Hashem's existence, and this may be one way to do so.
Yaakov blessed Pharaoh when he came down to Egypt- and from that moment on the Nile rose to Pharaoh's feet whenever he approached it. I assume that your neighbor is a nicer guy than Phraoh ;)
You'll also see that various great rabbis throughout history blessed the gentiles that they encountered.
Assuming that you're not Jewish (from the tags) then it would be fine and probably appreciated.
Jews try to avoid saying G-d's name in conversation, but according to some halachic opinions, saying it in English isn't problematic.
I don't know if this a proof, but I thought that I'd share a related incident: When I went to get a blessing for a Jew from one of the most renowned English-speaking rabbis of our generation in Jerusalem, he asked for the person's name. I gave the name, and he said that the name wasn't Jewish, and that he wouldn't give a blessing to a non-Jew.
Go ahead and say "G-d bless you" to anyone you feel you want to. No matter if your neighbour is jewish, non-jewish, idolater or faithful to Hashem. And say that whether he appreciates it or not. This is something that's coming from you. Would you hinder yourself from saying 'thank you' or 'good morning' to your neighbour because he is mysantropist and doesn't like to hear it? That's his problem. Another issue is when your neighbour is a bully and may insult you or hit you or throw cans of beer at you as they do where I live. In that case keep away from him. Nevertheless you must return to him and provide him assistance if a tragedy happens, such as an accident, ilness, poverty and he's in need.