I made this set-up for use with rimfire rifles and pistols but it will also work with airguns.
I have a metal target base that holds a couple of furring strips on each side. I took a furring strip cut to length for the horizontal cross piece.
Then I cut slots part way through the furring strip with a miter box. The slots are too wide to hold the playing card. So I use some other type of card stock or a piece of playing card, doubled over, inserted into the slot to take up the empty space.
The playing card is inserted into the slot with the extra card stock and it's held in place without the worry of wind blowing it over. Once the playing card is shot, it's easily replaced.
Because a level rifle is important for accuracy, I use a level on the horizontal cross piece to keep the playing cards aligned as much as possible in the vertical plane. The horizontal cross piece is held in position with a couple of cheap clamps.
I know that some of you are going to ask, "why don't you use a scope level and not worry about keeping the cards aligned in the vertical plane?"
I do use a scope level but I want everything going for me when I take the shot. If the cards are as close to vertical as possible it reduces the amount of time and effort cross-checking the scope level.
The photo below is for shooting with a rifle prone on a bipod or rest. When I shoot with the pistol the vertical furring strips are much higher and I place the cards about eye level.