We agree with the flooring contractors. Linoleum is a vinyl product that is designed for interior use. It will not stick, and it won't hold up to rain and prolonged exposure to sunlight. You're in luck though: there is a product designed to be installed in applications just like yours. The product is called Gacodeck and is manufactured by Gaco Western Inc. of Seattle, Washington.
Gacodeck is a seamless, skid-resistant, synthetic-rubber coating system that is applied directly over exterior plywood or concrete decks. Troweled on, it cures in place to provide an attractive, elastic covering for surfaces that are either floor and/or roofs. It doesn't soften under heat or become brittle with cold. It expands and contracts with the substrate. The manufacturer boasts that the product is tough enough to withstand heavy traffic, chair legs and roller skates. Gacodeck is available in a range of colors and textures. We have incorporated Gacodeck into a number of projects we have built and are pleased with its performance.
For more information contact the manufacturer at: Western, Inc. P.O. Box 88698, Seattle, WA 98188.