Your baby is used to being soothed to sleep by you. This is normal (and I believe healthy) in infants and young babies. At some point, however, it's important for babies to learn to self-soothe at bedtime (and nap time).
Nine months is a fine time to start the process.
Please give her soothing objects, e.g. silky-soft plush toys or a soft blanket during the daytime, and when she's in your arms for any reason, try to include the object. The idea is that she will associate being soothed with the object as well as with her parents. When she starts asking for the object or clings to it, she's got a helper to self-soothe. Let he cuddle with the object during your bedtime routine and in bed.
Then consider "Ferberizing" your baby. The Ferber method is basically a controlled comfort method of getting your child to sleep by self soothing, something every one year old child should be capable of doing.*
The basic steps to this method (better explained and outlined here and in the book) are
Prepare your baby for sleep with consistent bedtime routines. These can include a 'warning' if old enough to understand, tooth brushing, reading, rocking, and singing.
Put the baby down when they are calm/drowsy but not yet asleep. If the baby is drowsy and about to sleep before the routine is over, abbreviate the routine that night and put them down while still awake.
Once in the crib, say something ("goodnight/love you/see you in the morning"?) and leave the room.
If the baby cries, return to comfort the infant at progressively increasing time intervals with soft words, but without picking them up. (E.g. on the first night, soothe the baby after three minutes of crying, then after five minutes, and then each ten minutes, until the baby is asleep.)
On subsequent nights, return at intervals slightly longer than the night before.
There is a routine to follow if the child wakes up during the night as well without picking the child up.
This will be painful for all of you. She's not used to her parents not responding quickly when she cries (a very good thing early in development, but not as necessary now, especially when there is no threat (i.e. not hungry/wet/cold/tummy pain/other that needs to be addressed), and you are not used to hearing her cry, which is (and should be) distressing to parents.
Some people object to comfort objects fearing an unhealthy attachment to the object. To me, that is an unfounded fear. We all have comfort objects, even as adults: favorite comfortable clothing, particular music, a favorite chair, (a glass of wine), a particular side of the bed, etc.
*We didn't Ferberize our first until about a year of age. I personally don't agree with Ferberizing at six months. Babies and toddlers are individuals, not cookie-cutter replicas. Temperament matters.