Hi Rosewood,
You could try Woodward's Gripe water. It's a very old remedy for loads of baby associated things - hiccups, teething, colic, etc. Very natural, no sugar or alcohol and it's fine from birth. Our paed says it doesn't really help, but it's the only thing that stopped our baby's hiccups which were frequent during her first 3 months.
It's available at Mannings and is pretty cheap - $25-30 a bottle.