There are a few American Girl dolls, particularly modern dolls from the 2000s and early 2010s, who don't have canonical birthdays. Since I'm getting ready for my 20th birthday - on Tuesday - I figured I'd make a list and give the dolls who don't have a birthday their flowers!
Lindsey Bergman - born in 1991
Kailey Hopkins - born in 1993
Marisol Luna - born in 1995
Jess McConnell - born in 1996
Nicki Fleming - born in 1997
Mia St. Clair - born in 1998
Chrissa Maxwell - born in 1999
Gwen Thompson - born in 1999
Sonali Matthews - born in 1999
Lanie Holland - born in 2000
Kanani Akina - born in 2001
McKenna Brooks - born in 2002
Logan Everett - born in 2003
Isabelle Palmer - born in Fall 2004
Z Yang - born in 2004
Tenney Grant - born in May 2005 (theorized to be either May 6, 7 or 8)
Gabriela McBride - born in 2006
Willa, Camille, Kendall, Ashlyn, Emerson and Bryant - born around 2010
Gwynn Tan - born in 2015