I have a client who had cystine kidney stones every year for the last 20+ years. I helped him implement an alkaline diet to keep his urine alkaline. He tested his urine every day with pH strips to make sure he was staying alkaline. He has not had a stone since he made this change 3 years ago. A few foods incorporated to create urinary alkalinity are as follows:
Peppermint tea (make it strong, about double the normal dose)
Real Lemon juice
A few foods to avoid that would create more acidic urine:
Candy, and other processed carbs or processed sugar
If you also have kidney disease, avoid or keep watermelon to a minimum. It contains diuretic properties (helps you urinate more), which means it can make an already compromised kidney work harder.