Evie Laine (eh vee)–prefer the longer version below (Eveline)
Eveline Mary (eh veh line)–this would be my pick, Eveline is unique without being trendy, and Mary is a classic
Eveline Laine–these two names feel too similar to me
Delaney Charlotte–Delaney is not my personal style, but this would be my second pick
Delaney Cara–these two just don't seem to mesh for some reason
Eveline Mary! I think it's a stunning and elegant combination, and one I didn't expect to see. I'd personally keep Evie as a nickname, giving her the substantial Eveline as her given name. (Genevieve and Evangeline are other "Evie" sources...)
I agree that Eveline and Laine are too close and "l" heavy to work with each other.
Good luck to you! :-)