First, what is the duvet cover made of? If 100% cotton, it will take a deep stain from coffee initially, depending on the quantity of coffee used to the weight of cloth. This will rapidly fade with exposure to light and with washing, and as others have said it will smell of coffee and possibly also feel tacky.
If it is a poly-cotton fabric (as most are) it will only take a on feeble colour change and will just go a weary off-white quite quickly.
As others have said, dyeing a large one-colour item is always prone to a patchy result, as wear patterns that are not normally visible cause the fibres to pick up dyestuff at different rates.
On the other hand, you could have some real fun by dyeing it with a deep Dylon machine dye, and after drying draw on patterns with a metallic fabric pen, making it very original and detracting from any patchiness.
Or buy a new duvet cover.