I recently bought a specialized Stumpjumper 29 and its only been a few weeks but I've punctured the tire four times already. I think im getting the punctures from the trees and bark on the trail but is there any type of tire that is more puncture resistant that the stock one I have right now?
Its unlikely that the problem is your tire quality. Stump jumpers are not cheap bikes and come with pretty decent tires. Although a Kevlar belted tire might help, its likely to be a waste of money.
First up is what you are riding over. Bark, twigs and trees themselves are not going to puncture a MTB tire. Thorns, particularly dry ones, will. Even relatively small thorns (a couple om millimeter) will puncture a tire.
If you have punctured and have not removed the offending pointy thing, you will puncture again, this might be what has happened. Are the holes in the same place each time? This is the most likely reason for four in quick succession.
Are your punctures one or two holes? If two, you are getting "snake bites" from too low tire pressure - (well covered already, use search)..
If you are riding over thorns, then you need to buy thick heavy tires with a Kevlar belt. Light tires puncture easier. Also install thick, heavy tubes. This extra weight wil slow you down, but not as much as fixing punctures does. Consider going tubeless (the sealer also helps seal up puncture holes). You could also ride different trails - I have some locally that I avoid for this reason.
It could always be you just had a bad run of it......
Watch what you're riding over. Thorns, glass, and other sharp objects are obviously not your friends. Seems like a no brainer, but it's worth pointing out.
Ensure that there's not something sharp embedded in your tire. This is a common problem- you'll run over something that punctures your tire and when you change tube it's flat again not too long after. Sometimes this is due to whatever punctured your tube the first time still being stuck in your tire.
Keep your tire pressure up. If you're noticing two holes in about the same spot on the tube that resembles a "snake bite", you're getting what's called punch flats. This happens when the tire and tube compresses sufficiently between the ground and the rim to actually cut the tube. Increasing tire pressure can help alleviate this
Let your bike "float" under you. This just comes with practice, but if you get your butt off the saddle in rough stuff and let the bike move underneath you, the impacts aren't as severe and you are once again less likely to suffer pinch flats. As this technique improves you can also decrease your tire pressure if necessary.
Go tubeless. This may require a conversion kit, or your existing tires and tubes may be tubeless ready in which case you'd just need valve stems and sealant. If you're unsure about which is the case, ask the folks at the shop you bought it from. Keep in mind you can still go flat but it's less likely. MTB tubeless also limits the max PSI you can use, which shouldn't be a big deal as one of the benefits of tubeless is running lower PSI.
Chances are your tyre has something sharp on the inside, that is rubbing on the tube while you ride and eventually causing another puncture.
Fixing a puncture is not good enough. You also need to find out why the puncture happened in the first place, and solve that problem. Remove the sharp object from the tyre (usually it sticks through and then gets stuck in there) or if it's a pinch flat you need higher air pressure.
When replacing the tyre, always fit it so the label lines up with the valve stem. That way if you're repeatedly getting punctures in the same place you will know exactly where on the tyre to search for the offending sharp object that is stuck on the inside, causing repeated punctures.
Also check the wheel rim for anything sharp or damaged. But you have a new bike, so that's unlikely unless there was a manufacturing fault.
Get rid of the tubes and use Stans no Tubes instead. You'll save a bit of weight where it counts the most, but more importantly the tires will be self sealing. Well worth it, I think most mountain bikers use it and you've probably switched to it by now, but for anyone else that ends up on this page.
Here's a demo
In addition to all the comments about being careful, Continental that claims to have a puncture resistant tire. ProTection Apex https://www.continental-tires.com/bicycle/technology/mtb/protection-apex
I ride road bikes and use Continental Gatorskin on my bike. I have run over glass and not had them puncture. If the ProTection Apex are anything like the Gatorskin, they would be a good puncture resistant tire.