Old-fashioned classic floor cloth with linseed oil.
This method takes more time (mostly in drying), but if you want an authentic period piece, this is the way to do it. (Linseed oil is made by pressing oil from the flax seed, and was a common product for hundreds of years since flax is the plant that produces linen for cloth.)
Use good quality canvas, duck or denim, and wash to remove any sizing. The piece should be about six inches larger in both dimensions than the finished floor cloth to allow for trimming and hemming. Stretch the canvas, using staples or tacks on a wooden frame. Saturate the canvas with linseed oil, spreading the oil gently with a paint brush so that it does not puddle or drip. Make sure the oil penetrates through to the back side. You may need to apply oil to the back as a separate step.
Hang the canvas outside, preferably in warm, dry weather. It will take several days to a week to dry completely depending on the temperature and humidity. The linseed oil will stiffen the cloth as it dries and create a hard surface to the touch.
When dry, stencil or paint a design on the canvas using any of the following: natural pigments dissolved in linseed oil, artist's oil paints thinned so that they aren't lumpy, oil-based exterior house paint, spray paint (non-acrylic) or oil-based hobby paints. After the paints are thoroughly dry (allow 3 days, except for quick drying spray paints), seal the surface with a clear varnish. Apply at least 3 coats of varnish, allowing each coat to dry completely.
Cut the canvas from the frame with a razor knife. The edges can be left as is, or folded under for a hem, and glued with contact cement. Hemming wasn't often a worry with the old cloths, and varnish can be applied around the edges to seal any fiber ends. These floor cloths will stand up to foot traffic, but if you notice a wear pattern, re-varnishing is in order.