I think relishes tend to be a way of preserving food, so it makes sense they tend to be sour and sweet. I think it's hard to avoid if you want a shelf stable product.
You might have to go with a fresh made product that won't last as long. What do you want it to be used for? Sometimes I throw whatever herbs and some onions into a food processor with some oil, salt, and an ice cube. Always seems to work.