Usable range for iron sights?

I'm thinking of buying a springer with open sights such as the HW77 or the Beeman R9. I want to use this for closer distances (probably maximum 20 meters) on chipmunks around our front porch where I don't feel safe using the PCP. Is this doable with iron sights?

I have a TX200 that currently doesn't have a scope. Another option is just get a scope for that instead of buying another gun. I've been wanting the SWFA 6x fixed scope for a while now but it is expensive.
 
I use a diopter rear sight with the stock front sight on my R7. I find it good on 1" spinners out to 30 yards. Beyond that the holdovers get tricky, because the post covers the whole target. If I worked up a proper clicking range chart, it could be stretched further. The SWFA scope is a good idea also, I used a fixed 6x Leupold on my Ruger #1 .243. It is good enough glass to shoot clay pigeons on a 300 yard berm with. Perfect for a no nonsense deer rifle.
 
Totally depends on your skill and eyesight! There is no inherent range limit to any type of rifle sight.

The term "iron sights" includes both open "notch" sights, and receiver-mounted aperture, or "peep" sights. For most folks the latter are much easier to use and far more accurate, and a search here will turn up plenty of info. I use aperture sights almost exclusively....my effective range with notch sights is about the other side of the room, LOL. But again - that's me and my old cataract-ridden eyeballs, not the sight per se.

Finnish sniper Simo Hayha, the most successful of WW2 - about 500 kills against the Soviets - used the stock open sights on his rifle almost exclusively. (He ditched his scope after shooting a Russian sniper, whom he had spotted by light reflecting off the enemy's glass.)
 
A HW77 with open sights I fine for 20 yards and more. Put out a target the size of your prey and practice at the intended range. When you can hit it 10 out of 10 you are good to go.

Mitch

^^This. ^^
I will be zeroing in a new (to me) rifle tonight. 
it will be for shots at 6 yards. But whenever I’m pesting around my yard I hunt over a bait pile. So I zero my gun at that spot , from my shooting position. I make these cardboard squares. Put a 1” target dot in the middle. Then slide a bamboo skewer through the cardboard so I can stick it into the ground. 
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Completely depends on your eyes, your sights and how good you can shoot. I used to shoot empty .22LR 50 count boxes at 75 yards with open sights most of the time. Now I need a diopter if I want to shoot a much bigger clay pigeon at the same range and hit it sometimes.

I can Completely agree. When I was younger with good eyesight, I could also shoot out passed 50 yards at very small targets.I preferred the old-school front brass bead sight And rear U-Notch sight.And also liked The rear sites that had the white triangle at the bottom of the notch. 
 
A springer is good for around 3/4" groups at 25 yards with iron sights and me shooting. As long as the target is well defined. I was determined to bag a squirrel this past fall using a rifle with a Williams peep and front post. I had practiced until I could reliably get dime sized groups at 25 yards on a paper bullseye target. I took my rifle to my deer stand, waited till a nice gray squirrel showed up, shouldered the rifle, and the squirrel seemed to disappear. Took the rifle down, nope still there. Tried several times and just couldn't pick it up against the leaves. Went home, changed the aperture to a bigger size and went back to my stand. After a little while a big fox squirrel came in and stood up facing me. This time the post stood out clearly against that light colored belly and it was sayonara squirrel.

The point being that scopes have an advantage in many hunting scenarios where light is dim and the target can often blend into the background.