If a Muslim country becomes increasingly "less Muslim", it will cease to be a Muslim country, no? That then renders the question moot.
I think what you meant to ask for is a Muslims country that is not Islamist. Turkey for now, although I don't expect the Turks will slide towards theocracy. Morocco is one, although the monarchy's pace of democratic reform is glacial. Albania, I believe. Senegal and Mali are becoming more Muslim (in that the percentage of citizens who are Muslims has been steadily increasing over the last century) and also more democratic. Albania is the same way, coming out from a long Maoist shadow of official atheism. Bangladesh, although I'm not too sure about that one. And for all their problems, the Lebanese will rebuild their country again.
Again, they are all drifting towards the same result.
You seem to believe that a Muslim majority makes for an inevitable theocracy. That's your opinion, but the facts are against you.
It may be not, but a Muslim majority leads to other similarities. For instance, the heavily Islamist Taliban made the drug manufacturing and trade the main source of the regime income; and so did "non-Islamist" (in your opinion) Albania, and especially it's future province Kossovo. The difference is that Kossovars and Albanians diversify in other savory areas - the sex slavery being their specialty of choice.