I don't know why people think the two things must go together. I know plenty of highly religious people that are not moral people as well as non-religious people who are. As others have said, be a good example, talk to them about their decision making and talk to them about your decision making so you are modeling even your thinking for them.
If you are looking for ideas about books and resources to use, Aesop's fables have been around for thousands of years and are full of good nuggets and lessons for life in general (you'll likely remember the tortoise and the hare or the crow and the pitcher I believe). Of course, modern updates and takes on the fables can also be found. Additionally, most cultures have tales with lessons in them so any number of parables or fables can be used from around the world for these "ethics" lessons - any fable will do. You can even tell Christian parables such as the Good Samaritan without having to make it about the religion and just discuss the moral lesson behind the story.
As you read any story depicting protagonists and antagonists making a decision, you can discuss the possible outcomes to the decision together. Allow them to practice predicting consequences of a choice for themselves and for others and pretty soon they'll be thinking about decision making in a way that allows them to make informed thoughtful decisions whether they are determining to buy that new gadget they want so badly or something more morally based like whether to walk over and help the geek getting beat up by the bully right now.
Make sure you sit down for a daily meal together. The single most important determining factor in a child's social skills and emotional character is whether or not he or she has supportive and connected parents at home. Sure, you can use books about manners with them alongside those fables and other stories you read, but just modeling good caring, listening skills, and ethical choices will take you a long way. Hearing what is going on in their lives, what they are thinking about, struggling with, observing in friends. . . over a shared meal you prepared and are eating together is the best way to be sure their morals and the decisions they are making around those morals are aligning with your family values (and that your kids have good manners and social skills along the way too).