Japanese Muslims has an article that gives some useful advice regarding dawah in Japan which is applicable to any society where atheism is strongly pursued:
"One way we can spread the message of Islam in a soft way is to get involved in our community wherever we live, in a positive way. The community does not need to be an Islamic community only. We can help the poor and the needy, the old and the orphan and the homeless and the people in suffering and the list goes on and on. These rightful acts of ours will Inshallah change the way we are looked by the non-Muslim community members around us.
This becomes especially important in an atheist society like Japan where a certain stigma is involved in religious discussions. The Japanese people may not be very receptive to what you say about the Oneness of Allah, His most important attributes and Muhammad (May Allah be Pleased with him) being the final Messenger of Allah. However, they will be very positive if you become active in the community and extend help wherever it may be needed.
This phenomenon has been especially very prevelant during the recent eqrthquake and the ensuing Tsunami and the Fukushima Nuclear Disaster."
Original article here.