3D print a paint roller
While printing a roller stamp or rubber-roll from a flexible material such as [hard]TPU, [softer] TPE, or even a [super soft] foaming flexible filament is certainly possible. In any case, this would create soft, somewhat squishy prints. These prints will work quite easily as a stamp or woodblock printing stock, transferring ink from a pad to paper. The print pattern will depend a lot on how soft the stamp is: the harder, the sharper it will print. A massive roll of this material can behave akin to a rubber roll as one uses it in linoleum printing.
A foaming filament might be able to take a little paint in its airgaps, but it will never be as soft and contain as much paint as a foam lacquer roll - making it at best an improvised tool, or one that is chosen for a specific artistic purpose. It behaves more akin to closed-cell foam, while foam brushes and rolls from artist supply are typically open-cell ones. So if you go for a roller-stamp, you'll need to have an ink reservoir in the shape of a soaky-roller that isn't printed.
To top it off, it is nearly impossible to print a hairy wall painting roller: the hairs used in them can't be achieved with common print materials and slicers at the time. Even if stringing creates hair of similar dimensions, they are not affixed well enough to not get lost in the paint and can't be reliably created on demand.
Notes on pricing: One of the few options for foaming print materials is colorFabb, who was the first to offer such. Most of their foaming filaments cost around 50 €/kg, their flexible NinjaFlex costs about 80 €/kg.