Here's a link to an article about vegan organic gardening from The Vegetarian Site.

There's a list of 18 soil conditioners/fertilizers that is used in veganic gardening there, for example these three:

7.) Hay Mulches -Using a thick layer of hay to cover the earth will feed the soil with organic matter as it breaks down, suppress weeds, and encourage more worms to live in your soil. Put gardens to sleep over the winter and cover them with a very thick layer of hay mulch.

8.) Composted Organic Matter consists of fruit and vegetable rinds, leaves, and grass clippings. A compost pile consists of food waste, i.e. peels from the kitchen, that is covered by course material like leaves, hay, or grass clippings. The object is to create layers of food material alternating with covering material to allow aeration. When a bin is full, the pile is flipped and covered by black plastic or weed mat to protect it from rainfall and create heat. It can be flipped again after a period of time, so the bottom becomes the top. Cover again and within a couple of months, depending on climate, nature's master recycling plan will have taken it's course and you will have vitamin rich soil.

9.) Green Manures or Nitrogen-fixing crops - 'Green Manure' is a cover crop of plants tilled into the soil. Fast-growing plants, such as wheat, oats, rye, vetch, or clover, can be grown as cover crops between garden crops and then tilled into the garden as it is prepared for the next planting. Green manure crops absorb and use nutrients from the soil that might otherwise be lost through leaching and return these nutrients to the soil when they are tilled under. The root system of cover crops improves soil structure and helps prevent erosion. Nitrogen-fixing crops such as vetch, peas and broad beans (fava beans), and crimson clover add some nitrogen to the soil as they are turned under and decompose. Cover crops also help reduce weed growth during the fall and winter months