Any good way to make, say, a sour-grape or sour-apple ice pop from scratch? I’ve experimented with adding lemon juice or white vinegar (or both) to fruit juices; however, by the time I’ve added enough to make it sour, it no longer tastes like the original juice.
Do you want real fruit juice or are you willing to settle for sugary crap? If the latter, try mixing water with sucrose-rich drink mixes – daiquiri, green apple martini, lemon drop, that sort of thing.
I’d prefer to use real fruit juice… at least as the base. Maybe combining apple juice with sour apple martini mix will give something usable?
The problem is that most store-bought apple juice is intended to be sweet, so it’s made from sweet apples and occasionally even contains added sugar. You could get around that problem by pureeing fresh sour apples like Granny Smith and the straining out the pulp, but otherwise it’s pretty much impossible to get the balance of sour and fruity right.
The proportions in this recipe for green apple sorbet look like they’d be a good starting point.
You could definitely use a sour apple martini mix, but that would kind of defeat the purpose… it’ll be chock-full of artificial flavours and refined sugar. you may as well buy the pops from the store at that point. 
Lemon isn’t pure concentrated sour. Citric acid… now that’ll give you bite without removing all the original flavor. You can find it (usually) in the canning section at the local wal-mart or grocery store.
Ascorbic acid will also give sourness without compromising flavor. It’s quite potent, and safe (it’s Vitamin C, fer cryin’ out loud)
It’s available cheaply in powder form at home brew shops.
And you can buy it in bulk for chump change from soapmaking-type websites. (It’s used to make bath bombs, etc.)