Name a specific regular circulation US coin that is actually difficult to find in any grade.

1.If all it takes is money then it is not rare.
If it is not a coin made for regular circulation, such as patterns, it doesn't count.
Forget about naming "condition rarities".
Not many of them are there?
All glory is fleeting.
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I'll bet this was an interesting question before the internet existed.
1880 shield nickel (business strike, i.e. made for circulation) should get consideration - but you probably already know this.
17xx
Not too many at my local B&M
By "difficult to find", do you mean "does not come up at auction every year"?
1793 "strawberry leaf" large cent (3-4 known) [are you counting die varieties?; there are many extreme rarities]
1795 reeded edge large cent (6 known)
1802 half dime (about 35 known)
1870-s half dime (1 known)
1876-CC 20c (18 known)
1823 25c (19-22 known, plus 2 more proofs)
1870-s $1 (11 known)
1834 motto $2.50 (10 known, plus 5 more proofs)
1854-s $2.50 (12 known)
1870-s $3 (2 known)
1798 small eagle $5 (7 known)
1815 $5 (12 known)
1819 $5 (17 known, 3 varieties)
1822 $5 (3 known, only 1 in private hands)
1828 $5 (13 known)
1829 $5 (15 known)
1854-s $5 (3 known)
1798 $10 (32 known, 2 varieties)
1875 $10 (14 known, plus 9 more proofs)
1920-s $20 (8-12 known) [many late date $20 coins were made but many were melted!]
1921 $20 (15-18 known)
1927 $20 (15 known)
1927-D $20 (8-11 known)
1929 $20 (60 known)
1930-s $20 (25 known)
1931 $20 (18-20 known)
1931-D $20 (30-35 known)
1932 $20 (22-25 known)
1933 $20 (10? known)
I could keep going; it is kind of a judgement call about the auction frequency since I don't have an actual huge table of data to crunch for that.
Th 1802 half dime is borderline, because there are many low grade damaged specimens that do come up at auction, so it might have a frequency of 1 or more per year. It is pretty much a "you can buy one if you have the money", but you might have to wait a year or two. It's been estimated that there are about 35 surviving specimens.
There are also the "really difficult to find" coins, where some were made, but nobody has ever found one.
Like:
1873-s no arrows 50c (5000 made, likely all melted)
Guess you can throw the 1933 Double Eagle out there....at least temporarily.
We all might get our chance at some point!!.....or we may all end up fighting over the one legal one.
Do you mean non-varieties?
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As someone who actively collected mint state shield nickels back in the 1990s I have a very definite opinion regarding the 1880 Proof vs. MS. It is my opinion that they can be distinguished and that the "MS" should command no premium as a result. I am sure many will disagree with me on this point.
[I take it back -- there are actually a handful of examples of the issue I named available right now!]
I am not following 291fifth argument, that if they can be determined,(which in most cases they can) then MS 1880 should command no premium, if this is true, then none of the other key dates where proofs can be had for minimal expense should be treated the same 1877 indian, 1885 liberty , etc . Rick Raff stated several years ago, theat several of the dies used to strike 1880s actually struck both formats.
yosclimber has a great list that includes the extreme rarities, especially the early $5's.
These are not in the same league, but they are very difficult to find - 1800, 1801, 1802, 1803, and 1804 dimes. These are about as rare as 1794 dollars, with the 1804 dime even more rare. For the collector, it is a chance to get a truly rare year at a fraction of the cost of better known "rarities." I collected these for a number of years and it is impossible to get a matched circulated grade set, such as VF30.
Nice group from yosclimber!
A couple to add: (and I've probably forgotten a few)
1831 half cent (if you believe business strikes were made) - 19 or so known
1873-CC No Arrows dime - 1 known
1873-CC No Arrows quarter - 5 known
1842 Small Date, Small Letters reverse half dollar - 4 known
1853-O No Arrows or Rays half dollar - 4 known
An authorized PCGS dealer, and a contributor to the Red Book.
Collectors need to make their own decisions. I made mine back in the 1990s and declined to pay any premium for what were claimed to be MS 1880 nickels. I just bought a proof, paid the much lower proof price and moved on.
Pretty much any 1880's 3c nickel piece after 1881.
1870-CC quarter
1871-CC quarter
1873-CC quarter (arrows)
"Everything is on its way to somewhere. Everything." - George Malley, Phenomenon
http://www.american-legacy-coins.com
@291fifth I know the island reverse isn't set in stone, but what is your opinion about it?
Ahhhhh...the stuff that dreams are made of
2009 nickels. Or have I misinterpreted the original question.
Insert witicism here. [ xxx ]
That pretty much eliminates all coins that are not unique.
What is the "island reverse"? I don't recall hearing that term before.
Ok, that's fine, but the Proof version is not a coin 'made for regular circulation', as you stipulated in your requirement to identify coins that are difficult to find in any grade. I stand by this example.
@291fifth It's a die marker on the reverse or the coin that both TPG uses to grade the 1880 as a regular strike, thought not everyone agrees with it.
I have my doubts about such things. It wouldn't convince me to pay a premium or advise anyone else to.
That list of Saints on Yosclimber's list is out to lunch. Only 60 known 1929 Saints? There are probably multiples of that in currently existing slabs. Most of those numbers on later Saints don't correlate to any rarity listing I know of...and don't even fit with PCGS's estimates.
1874-cc dimes.....much, much tougher than the more well known and much loved 1804 dime. 50-100 known?
1878-s halves - estimates seem to range from 35-75. The 74-cc dime could be rarer.
1872-s quarters - 100 to 150 known is a fair estimate though I think on the lower half of that range.
1844 Orphan Annie Dime...............................................................................................................just kidding.
Those "known" numbers are from Breen's Encyclopedia (1988), so some of them may be outdated.
Ouch. I'll say they are outdated. The pop reports have turned many a "so-called" rarity into an obtainable scarcity. Had Breen spent just 15 minutes with any top collector or dealer in gold back then, he would have had much more accurate numbers.
The 1873-S Liberty Seated dollar, 700 minted, none known.
Have you checked your great-great-grandpa's attic lately?
My Adolph A. Weinman signature

1861-S Lib $2.50, 24,000 mintage, seldom appears at auction.
1858 Lib $2.50 with a mintage of 47,377 should be fairly easy to find but few ever appear at auction or dealer inventories.
https://www.pcgs.com/setregistry/gold/liberty-head-2-1-gold-major-sets/liberty-head-2-1-gold-basic-set-circulation-strikes-1840-1907-cac/alltimeset/268163