Vinegar is a biodegradable natural agent which will kill plant material; normal vinegar for putting on your chips (fries) contains about 5% acetic acid and is produced from grapes, apples or grain by fermentation in anerobic conditions. This weaker product works on some young weeds, but higher concentrations produced by distillation (15%) and freeze evaporaton (30%), are needed for a more effective herbicide. The vinegar degrades after a few days so any increase in the pH is only temporary. Best results are obtained if it is used hot and repeated for three days. Concrete and stone can be hosed down after treating to reveal their true colour.
Corn Gluten Meal which is a byproduct of the wet milling of maize. It works by preventing the germinating seed forming roots with no effect on existing plants or seedlings which have developed roots, so it has limited uses. The main one being as a weed and feed treatment for lawns since it also releases about 10% Nitrogen as it breaks down. Of course it is also limited in availability as most maize production is in North America, and it is used in animal feeds as well.
Found the above from an organic gardening site. I'm sure you can buy some weedkillers that are safe to use with animals but we normally end up pulling them out. Have docs and nettles growing through the fence at the end of the garden - they are a nuisance.
