It is hard to give advice without really knowing what you do to put your baby down. However, I'll make a couple of suggestions and hope that at least one will help.
First, are you sure you are giving your baby enough time awake? At 9 months, most babies need about 3 hours of awake time in between each sleep period (my son actually needed a bit more - like 4 hours). 9-month-old children also only need about 3-4 hours of total naptime a day. Make sure your daughter is not napping too close to bedtime, or sleeping too long during the day (every child is different of course - those times are best used as guidelines).
Next, are you careful to wind down before bed? At least an hour before bed, it is time to stop playing exciting or stimulating games. This means different things to different kids, but if your baby gets excited by electronics, take them away at this time. If the baby relaxes when reading, it's time to pick up a book. Do you have a bedtime routine? With us, we take a bath, have a bottle, brush our teeth, read a story, and say our prayers, and then we turn on his sleeping-time CD every single night. This routine helps prepare your child for sleep, and soon she will figure out that bathtime indicates bedtime is coming, which will help her relax before it is time to sleep. My son cannot sleep with any music besides his sleepy-time CD, now, but the moment I turn that CD on, he is yawning and rubbing his eyes.
Also, don't just leave your child to cry. The CIO method must be tempered with an attentive mommy. For me, every 10-15 minutes, I would go upstairs, lay my son back down and give him his paci, and then leave. No eye contact, no words, but still a sign that Mommy is there and knows she's trying to sleep. And one of those times, he just wouldn't get back up again.
Finally, to help with your son, you might consider putting your daughter to bed a half-hour or so before your son goes to bed. He's older and can stay up a little bit longer, and this may give her some alone-time in her room to relax and sleep without him there.
As a note about the other poster, I have never heard of it being illegal for kids of either gender to share a room at this age, before puberty has even hit. Sheesh.
I hope one of these techniques will work, or help you out. Good luck to you.