Not a fan of Piper, but Ivy is nice. Others: Iris, Mariah, Violet, Isla, Eliza, Diana, Sarai, Caroline, Lorelei, Eileen. There's also Delilah, but I can't get past the Biblical story/association. (Lorelei the siren has its issues, too, but I know so many little Loreleis that the association is pretty faded.)

Madeleine, Emmeline, Adeline, Carolina, Briley, Riley, Kiley, Isis, Calliope, Maya

Dina is often pronounced Dee-na.  You are more likely to get your desired pronunciation if you spell it Dinah.

Ida? Irene, especially with the I-ree-nee pronunciation?

Maia

kaia

lyra

majken

My new baby girl is eilis (with an accent on the second I) pronounced eye-lish. It's gaelic for Elizabeth. 

Since coming to this wonderful site, I've learned that long I names are trending. Any thoughts on why? I think somehow the long I is quite strong and dignified, not too cutesy. Do you hear it the same way? 

Blythe

Bryony

Diana

Hermione

Iona

Myra

Sapphire

Titania

Viola

Twila

Eliza, Isla, Miley, Riley, Maya, Ira

I grew up with a girl named Aislee (pronounced Eye-Lee)

My daughters are Meika and Violet, both with the long "I" sound and I have thought about continuing that pattern should we ever have a third daughter.  I don't have any additional ideas, but in have enjoyed reading all the ones posted already and wondered if there is a way to easily refer to this thread in the future should I ever need to :).  Ivy and Piper are lovely names.  I like them both.

I love the name Isla or Iris.

Another idea is:

Islette (pronouced Eye-lett)

Lyla

Violet

Mia/Mya/Maya

Eliza

Skye

Kyra/Kira

Myra/Mira

Ida

Lorelei

Marika 

Skylar

Ayla

Ryan (becoming more commonly a girls name)

Aileen

Kylie