In the App Store (for $0.99, USD) is an app called Touch Icon Creator. With it, you can create icons based on images in you Photo app.
What I do is save a good picture of the web site (or the company's logo) and then use the app to create the icon.
It helps you make icons that look as if your bookmarks were professionally designed. Of course, there are other icon creator apps, but this is the one I use/like. YMMV.
Marilyn