Hi J.,
Been there....I, like you, did not like my kids on the steroids; sometimes it cannot be helped.
I have two kids (now adults) with asthma and found, after many discussions with their pediatrician who by the way specializes in asthma, that a strong cup of coffee with a flavored non-dairy creamer could help fend off an attack as well as aid in preventing them. The caffeine helps to open their bronchial passages by doing exactly what the prednisone does: reduces the inflammation. My kids were on daily maintenance inhalers and I would give them two to three cups of coffee per day. BTW - Children's bodies react differently to coffee than that of adults so you don't need to worry about hyperactivity or their inability to sleep.
I also found minimizing their dairy intake (particularly milk, ice cream & yogurt) was a big help in reducing the number of attacks; especially when they experience consistent episodes. Also know that allergy, cold & flu season can trigger attacks and so you may want to have her tested for allergies as this will help minimize her episodes. Lastly, I found keeping a humidifier in their rooms at night helped.
Just in case you have Kaiser my kids pediatrician name is Alice Yen. Although one of my kids is an adult she still continues to see Dr. Yen (Kaiser now allows a child to continue with their peds doctor through college). She's at the Milpitas facility and is very good with asthmatic children.
I hope you find this information helpful!!
Connie