The Sunbrella Graphics System works really well. There are also professional screen printing solutions that perform ok.
For the hobbyist, or when on a limited budget, high body acrylic artists paint (Liquitex, Golden, etc.) can be used with a degree of success. More liquid acrylic can be used (Nova, etc.), but they are harder to handle and have less plasticizer, resulting in a less flexible film.
The best technique is to mask the graphic, then stipple the paint on to avoid seeping through the mask. Do not thin the paint, Sunbrella is an acrylic material (plastic), so nothing "soaks" in. Using a stencil brush or stiff fitch, "pounce" the paint on in a thin layer, allow to dry to touch, then pounce again until coverage is obtained. Do not let the paint build up; it will crack.
Use the same color paint as the awning for a first coat, or, alternatively, use clear gloss medium until the edges are sealed (gloss is more flexible than matte). Keep at it until the desired coverage is obtained, and when dry to touch, carefully remove the stencil. Do not let it dry too long, or the paint will tear when removing the stencil. I have had awning graphics last 5 years plus using this technique.
I would not use alkyd or latex paint; both will likely suffer from plasticizer migration, and are likely to crack and begin to fail in short order.
https://www.sunbrella.com/en-us/textiles/shade/collections/sunbrella-graphics-system