Make your own oilskin using white spirit also known and mineral spirits in the U.S and linseed oil.

White Spirit is also known as mineral turpentine, turpentine substitute, petroleum spirits, solvent naphtha (petroleum), varsol, Stoddard solvent,[4][5] or, generically, “paint thinner“, is a petroleum-derived clear liquid used as a common organic solvent in painting and decorating.”

“Owing to the volatility and low bioavailability of its constituents, white spirit, although it is moderately toxic to aquatic organisms, is unlikely to present significant hazards to the environment. It should not however, be purposely poured down the sink or freshwater drain.”

Thanks Wikipedia

2.2 Environmental levels and human exposure There are few data on white spirit in air, water or soil. Monitoring at a site contaminated with spilt white spirit (Stoddard solvent) revealed soil levels of up to 3600 mg/kg and deep soil water levels of up to 500 mg/litre. Biodegradation led to a 90% reduction in soil concentration over a 4-month period following remediation.

inchem.org

Next you need to mix some simple chemicals. You will need one quart of mineral spirits (You are not wanting mineral oil. Mineral oil will not work), which is available as paint thinner at Lowes, Home Depot or any paint store. You will also need a quart of boiled linseed oil. It is available at the same place. If you go to Sherin Williams or Porter paints you can get tarp and chemicals at the same stop.

Mix the mineral spirits and linseed oil 50/50. Shake it up good. You need the combination of chemicals. The linseed oil waterproofs the fabric and the mineral spirits allow the oil to dry. If you use straight linseed oil the fabric will never dry and will remain oily and sticky forever. (At this point you can also add pigmint if you want color in the tarp.)

Hang your prepared tarp from a clothesline or the back yard fince and paint it with the solution. Make sure it is saturated well. Leave the tarp hanging untill it dries. With the 50/50 mixture it will take about 48 hours. It will take the smell about a week to disperse.

Thanks Wilderness Safari