I'm particularly looking for remedies that would be safe for children between 1 and 5 years old.
For a immediate fix a steam session is quite helpful for opening up the lungs and make the child more comfortable.
It's also important to learn what sets off an attack in your child, so you can avoid those stimuli. For example running in the cold gives me an attack every time, so I avoid it if at all possible. Others I know have allergies that trigger their attacks, both food and atmospheric.
Above all remember that Asthma can be lethal, and it's better to be medicated than dead.