The pellet bow is a real-world weapon. It's basically to the sling what the crossbow is to the bow and arrow & thusly should be a simple weapon. (Pull back the bow and release.)
I believe the stats should be
Simple weapon
1d6 damage, crit 20/×2
30' range, standard sling bullets for ammunition
25 gp cost, 2 lb. weight
Are these balanced?
This is a small-game hunting tool, not a weapon. The pellet threatens only soft-tissues and eyes. Stat it like a strong blow-gun, not a stronger sling.
Regarding the stats, I think that they're too much for a simple weapon with ammunition. You've statted a short-bow with a poorer crit multiplier and shorter range. I'd make it martial, but I think that it's unrealistic as an actually threatening weapon. (See below)
A sling is actually more difficult to use IRL than a bow; you have to load it with a bullet or stone, whirl it without hitting either yourself or an adjacent ally, and release it when it's 'pointing' slightly off of your intended target. Only the idea that 'throwing rocks' is easy, and that the materials are ubiquitous makes it a 'simple' weapon.
Additionally, the sling's action, coupled with the mass of the bullet actually imparts significant momentum to the projectile when hurled. The damage from 2 to 8 Oz. of lead, clay or rock is quite impressive.
A bow shoots as far as it does because the flights on the arrow, coupled with the arrow's shape, make it so much more aerodynamic than a bullet or stone, that it acts much like a glider. However, the momentum of a slung stone is such that it can rival, or even surpass, an arrow for distance.
This pellet bow appears to be at least as difficult to operate as a bow, but must use lighter pellets than a sling. The damage, if verisimilitude is a goal, should be lower and the range shorter than that of a sling, due to the necessarily smaller mass of the projectile, with no increased aerodynamics.
The weapon would be useful for small game or varmints, but much less so versus any large game or armored opposition. Think of the modern 'Wrist Rocket' sling-shot. It's useful versus a rabbit, but you endanger only a person's eyes or soft tissue. A sling, capable of lofting projectiles so much heavier, can break bones and cause significant damage to skulls or internal organs.
It’s better than the “prodd” from Dragon vol. 349, which is a crossbow-like weapon that shoots sling stones. The prodd is cheaper (20 gp) and has a longer range (80 ft), but it also weighs more (4 lb.) and deals less damage (1d4).
But the main difference is that the prodd, as a crossbow, requires a move action to reload. That makes your pellet bow massively better. In fact, all simple projectile weapons require a lengthy loading procedure. Adding a simple projectile weapon that does not seems inappropriate; it would eliminate a lot of the point of things like the shortbow.
The stats may be "balanced" (if anything, it's actually a less effective than a sling or a shortbow), but I disagree conceptually with some of the stats you've decided on. After some quick reading on operating a pellet bow - it appears to be more difficult than a standard bow - in order to have the ammunition avoid impacting the bow on release, it must be held at an angle, instead of pointed at your target. I don't know that i'd call it an exotic weapon, but I would definitely categorize it as martial - especially since standard bows are martial weapons.
As for the damage, if we operate on the premise that the pellet bow is to the sling what the crossbow is to the bow, then I think your damage is spot on. An arrow from a Medium-sized bow is 1d6 for a shortbow and 1d8 for a longbow. Their Crossbow equivalents increase the damage by one die type: a light crossbow deals 1d8 damage, and a heavy crossbow deals 1d10 damage. So mechanically, I think it makes sense to increase the sling's 1d4 damage to a 1d6. Also the damage type should be Bludgeoning. Rocks don't strike me (pun intended) as having an increased critical modifier, so let's keep your 20/x2.
Next, for range, a sling's range is 50', so it seems odd that a a pellet bow's range would be reduced to 30'. Instead, I would increase it. If we go back to the crossbow analogy, we should be adding 20' to the range (bringing it to 70'), but I dislike that from a physics standpoint. Instead, I'm going to look at a javelin's range (hand powered) versus a bow's range (tension powered). A javelin has a range of 30', and a shortbow has a range of 60'. Now, there's clearly a difference in the mass being propelled from an arrow and a javelin, but D&D isn't a physics simulator, so I'm going to ignore it. So adding on 30' doesn't seem too unreasonable to me, giving our pellet bow a range of 80' - just over the range of a shortbow, and just under the range of a longbow.
Finally, for price & weight - the creation of a pellet bow seems to me that it would require a similar level of effort, skill, and materials as a standard shortbow, so I would charge the same amount - 30gp. It likely weighs the same, so 2lbs seems good to me.
Like others here I might leave the basic Pellet Bow as doing damage like a blow gun. (Maybe a bit more if you fire caltrops of some sort instead of pellets) I might also have it give a +2 Bonus on Survival checks for hunting.
That being balance for realism of course.(If not for that I'd say your stats are probably fine.) If that does bother you and you want the same concept but with more damage I see no reason that one couldn't make a Pellet War-bow, or probably warcaster (read crossbow), that does more damage. I'd say those would probably be exotic weapons and need some additions to concept to be functional. My ideas below aren't super well formed (I'm at work and writing quickly) and they'd probably necessitate some heavy gearwork, unique materials, and custom engineering elements that may not make them readily available (read expensive) but as a DM I think they could be given decent reasons to exist in the world and possibly meet your interests.
A Pellet War-bow would either need to fire a larger ammunition at the same speed or have some sort of additional aid to create an incredibly strong pull that likely would slow down its rate of fire. Really the first would necessitate the second. I'd grant a Pellet War-bow probably a d4 damage with a 20/X3 crit range, but (and this is a bit to balance its new feat requisite as well as to underscore the additional firing aid) I'd also let a person add 2xSTR Mod to damage. I'd probably say it only gets one attack a round unless a person's STR is a high number.
The Pellet Warcaster could fire the original bullets but necessitate a crank draw and some crazy tense string to be damaging.(Frankly you'd be making a very early version of a gun with custom crossbow cord. There's probably Mythbusters busting this concept) I'd up its damage to d6 with a 18-20/x3 crit range to underscore its puncturing power. Reload would be a move action to crank. For quicker reload I'd probably say a good STR and a moderately high DEX. Harder to get but possible for a Fighter focused.
