In a food processor or blender combine 1/3 cup of the oil, the basil, almonds, coconut, cheese, and sugar. Cover and process or blend until nearly smooth, stopping and scraping sides as necessary and adding enough remaining oil until of desired consistency.
If the pesto is not to be served immediately, divide it into three portions. Place each portion in a small airtight container. Refrigerate up to 24 hours or freeze up to 3 months. Makes about 1-1/3 cups pesto.