What are hunting slingshots? Most slingshots have enough energy to take small game and pest with a good hit at short range. So most can be used as hunting slingshots.
There are different bands/tubes which can increase your killing power to some extent. The trade-off is that their power often comes with a harder pull.
I use the heavier pull Trumark black tube bands for hunting sometimes when I'm sure I'll only get a few shots. I can pull them ok, but I have trouble holding or griping the pouch after about 20 shots. I use their red tapered or gold regular bands most often; especially for practice.
I like white marbles for back yard shooting when they can be easily recovered. I use the small 1/4 inch steel ammo for plinking where ammo is lost. Either will also work for pest birds or small critters up close.
Larger 5/16 or 3/8 steel ammo is better for small game hunting. I think heavier lead ammo like 000 buck shot is even better.
A decent slingshot can cost less than ten dollars. Keep it simple. You don't need an expensive, powerful, or sophisticated model. Simply get one and practice, practice, practice... try different holds and styles of shooting. You can decide if you want something different with some experience.
Slingshot Advantages! I sometimes hesitate to have firearm or even a bow handy because of safety, the laws, or loosing it to a thief. I don't hesitate to have a slingshot handy in my truck, boat, house...
I can shoot very quietly almost anywhere. Few people view the slingshot as a big threat. The bow-n-arrow is more dangerous. Air guns look like firearms.
I sometimes shoot in the tiny backyard at my apartment. For an ammo trap/backstop I simply scrounged around the apartment. I used an old arrow, two lanyards, and a hand towel, but many other things could work. I hang it in the corner of my fence.
The towel has four safety pins holding the bottom together. I use another safety pin in the center for an aiming point. It easily stops the white marble practice ammo. They drop to the ground and can be shot again. More serious ammo would need a more serious backstop.
Update: I've found a coat hanger works better than the arrow and lanyards. I now hang it close to the ground and the marbles stay close and are easier to pickup/find this way.
The hunting slingshots are "a perfect fit" for the traditional bowhunter. When shooting, drawing, holding, aiming... hunting slingshots are similar to the traditional bow.
I make a conscious effort to shoot my slingshots like my bow. I believe the slingshot practice is helping my bow shooting. I'm using many of the same finger, arm, body muscles, and movements.
In the picture on the right I grip the ammo pouch almost the same as the bow's string. This gives me almost the same anchor, cant, arm position... as when shooting the bow.
The advantage is my shooting stance, anchor point, target acquisition... are very close to the same as when shooting the bow.
There is no ammo and the bands are not stretched in the pictures.
Note this "bowhunter" pouch grip works best with the larger practice marble ammo. I sometimes use my thumb pushing on the side of my first finger for more gripping power. I can't hold it this way when using small diameter ammo and powerful bands.
Hunting slingshots bands are important, they do the work, supply the power, and they're not all the same. I've only used bands from three companies; I like those from Trumark. Their bands are good, and the ammo pouches are especially good.
Some ammo pouches are too stiff and slick. The ammo has a tendency to slip around. The Daisy bands I tried had an ammo pouch of stiff leather. It is much easier to hold the ammo in a soft leather pouch which wraps around it.
Trumark's amber colored standard bands are hard to beat. Their black bands look better, last longer, and shoot a harder, but they are considerably harder to pull and hold.
I like Trumark's red tapered bands, but I've only owned one set. They're hard to find locally. The red bands seem to give the best velocity for the amount of pull needed, especially with lighter ammo. Update: I have now switched to the red bands on almost all my slingshots. I still have heavy black bands on one wrist rocket I keep in the truck.
My slingshot game bag last season was a couple of quail taken with a cheap $3.00 slingshot while deer hunting.
Read: Slingshot Hunting!
I've also taken nuisance birds, lizards, grasshoppers... I'm excited about using my "bowhunter's handgun" on small game this year.