I sliced up @HudsonStan's holder in Slic3r to use a lot less filament since I had no need to hold the filter separate from the press. (I use a metal filter, so I like to keep it in so it doesn't get lost.) Also chopped off the edges to make it use less filament.
It took two hours to print at 0.5mm resolution with two perimeters and 15% cubic infill and used around 20 meters of filament.
You want a strong infill because the only orientation to print this without support is not naturally resistant to snapping when under load (the prongs can easily snap off along their layers).
It's held to the wall with 4 pieces of 3M Command Velcro and I put some quake putty on the top to prevent slippage (my tiled wall is decidedly not perfectly vertical).