How can i find down my daughter day of birth , she was born there in 1986

That is going to be very very difficult. HIPPA makes it nearly impossible

Pretty sure it opened in 1989

I don't believe you can. Since she is over 18 and privacy laws are in place i.e. HIPAA; they will not provide records without her consent and date of birth is protected by that law. They are part of the Centura Health Network, so you would need to deal with them which IMO would be a waste of time due to strict privacy laws meant to protect us.