Obviously, CZ's are getting the majority vote. And who can argue with them? Accurate and reliable, they are phenomenal rifles for the money. But, the OP did say:
What is the most accurate 22 LR rifle under 500 bucks and suitable for small game hunting?
Now, that statement covers a LOT of ground. So let me take the liberty of listing a few of my preferred "small game guns", in no particular order:
1. The venerable 10/22. The 22 that has been killing game well since the 60's. Mines a Mannlicher version, and is accurate enough with Williams receiver sights to knock off squirrels at ~60 yards. And, it cost around $400 brand new. The carbine and sporter versions are well under that.
2. Henry H001. The standard Henry 22 carbine. Plenty accurate enough for hunting, I have used mine often hunting with dogs since its light, easy to carry, and holds 16 shots. Wally world price is around $300.
3. Old reliable - Marlin 60. One of the most accurate auto 22's ever made IMHO. My older version holds 18 shots if I remember correctly, and wears a small Simmons 4x scope. It is easily capable of 1" groups at 50 yards, and best of all, can be had (used but in good shape) for $100 or less at most any LGS or pawn shop.
4. New Haven 251c - My grandpa's old gun. Made by Mossberg in the 60's and 70's, its a quirky little gun. Loads 15 shots through the buttstock, has a decent trigger, and will absolutely drive nails. It wears a 1.5 x 4.5 x 32 Bushnell, and will group 5 shots under 1" at 50 all day long. My most accurate 22. They can be had for under $200 on the used market.
5. Browning ATD - Lightweight, accurate, and dependable. A fine little gun that anyone can shoot. Mine has stock sights and is minute of squirrel head at 40 yards. That's plenty good enough for me. The downside is they are pricey, but can still be had used for under $500.
Honorable mention - Romanian M69 trainer. Very accurate little bolt gun. They can be finnicky to operate if not kept clean, but overall I've had no complaints. They can be scoped but you have to have them d&t'd for the mounts as I've not found any that would fit the little grooves on the receiver. But they can be had, at least locally, for ~$100.
The guns I've listed are by no means perfect. They all have their flaws. And some are more accurate than others. But as a rule they fit the OP's criteria, and furthermore are very affordable. Sure, there are other guns that would fit the bill, but the ones listed are what I own and have experience with. I'm sure there will be several who disagree with some of my statements, but again they are based on my particular guns. I guess if I had to pick one, it'd be the 10/22. They are the MOST reliable, and the DECENTLY accurate (mods not withstanding) in stock form to do what the OP, or anyone else, requires. And, the are very easy to maintain and modify. The sky really is the limit as far as how much one can spend on a 10/22 and it's modifications. I prefer to keep mine mostly stock, and the example I gave has only had the trigger and sear surfaces stoned, trigger springs replaced, and a flush mag release installed. Others have made them into 1/2 moa guns. I'm not that picky as all I do is hunt and plink with mine. Well, with any of my rimfires for that matter. Hunting and plinking is what they do best.
Hopefully, some of you can get some use out of these ramblings...
Mac