my friend's ds didnt sit unaided till she was 9.5 months. She almost looked as if she was unable to sit up.
One day she didnt want to sit, the next day she sat. It will happen!
try sitting on the floor with her regularly - she will start to copy you, and she'll want to sit up too. Have you tried putting her in the "frog" position? i.e. sit her on the floor, then place her hands on the floor between her legs/feet. her hands will take her weight and will balance her.
Also, put a favourite toy in front of her, and she may well lean forward for it.
You asked about strengthening the muscles. My health visitor told me to put my ds on his tummy as often as possible, as their neck muscles are built up by doing this. this helps develop their balancing skills too.
good luck!