HA! I recently saw that in a study, plain ol' honey beat cough suppressant in its efficacy!
The lemon and honey is a great standard! I also find it helpful to massage in little circles on the sternum...starting at the top and moving down gently- imagine you are moving the chi down the chest, as thought subduing it.
Eucalyptus oil is great for breaking up congestion...and rosemary is awesome...not so harsh, powerful antibacterial properties. For a child, I might put some in very hot water, then have the child lean over the bowl of water and cover his head in a "towel tent" so the oil would be inhaled in the steam. Very very soothing!
Coffee of tea will also act as an expectorant...breaking up mucus in the chest so it can be expelled. This is when a strong cough is good....gotta get that stuff out!
At that stage, forming the hands into 2 "cups" and then gently tapping/pounding on the back over the lung area will break up phlegm. Cystic Fibrosis patients would be familiar with this.