craftgrrl | Felt Features for Plushes

I'm making some plushes and the person who ordered them want felt eyes and mouths. In all the plushes I've made before, I've only used button eyes and maybe embroidered a crappy smile.

The fabric of the body is regular cotton. I was wondering if anyone had any good ways to attach the felt facial features, in a way that they would last? I was thinking of possibly glueing them on (but with what type of glue) and then adding some stitching around since I wouldn't trust just the stitching.

So what type of glue would you recommend for attaching felt to cotton? And do you have any other suggestions for what I could do?

Thanks!