I'm an ordinary guy.
My target audience is likely to be people who are have deep theological questions and are scouring the Internet for answers. They need to know that I am offering information that they can trust.
Obviously, I'd like to incorporate the idea of a dead tulip. Possibly picking the petals off of a tulip. I'd also like it to contain the phrase "Dead Tulip" and possibly a tagline of "Picking the Petals Off False Doctrine".
The main problem is that I don't really have in my mind what a strong logo for an organization called "Dead Tulip" would even look like. That's where I need the help.
It needs to be intellectual, serious, strong, clean, professional, and trustworthy. While it will be used for a critical website, it should not seem angry or combative. Neither should it be morbid in any way.
Just keep that in mind when you're designing.