Being an atheist in a religious culture is a challenging situation and being an atheist parent is an even more daunting position for one to be in. Have you ever asked yourself how you can be an atheist parent?

[edit] Steps

Raise them however you want. They're your kids. There are worse kids out there. You'll probably do more harm worrying about every little thing.
Get them involved in activities that they like, and let them blossom into who they are. Let them know that who they are is perfectly okay.
If you can find other atheists and get help, cool, but if not, don't worry about it. Having diverse friends and family is good for children of all kinds to learn from.
Set a good example

Teach them why you are an atheist
Show them why honesty and responsibility is important
Expose them to things they will hear from their peers when criticized for their (lack of) beliefs

[edit] Tips

Get your children involved with environmental issues or volunteering; something that can help them feel as if they're doing some good without having to fall back on a belief system.
Teach your children to believe in themselves. Help them become self-sufficient and be an example of self-sufficiency for them to learn by.
Be an example of tolerance and acceptance, and let your children know that there will always be those who disagree but that doesn't make anybody better or worse than anybody else.