I had worried about coins’ ages affecting their mass, too, which was why I was tempted to go with volume first.
The two most relevant dates for that line of questioning are 1965 and 1982 – by 1965, none of the coins we’re considering* contained any silver; in 1982 the penny was changed from 3.1g to 2.5g. I suspect that the very small percentage of marginally-heavier “silver” coins is going to disappear in the noise of normal coin distribution; note that the theoretical distribution galt worked out and the observed distribution from Bergebo vary by more than 2% in mass.
If we assume that all coins minted in the last fifty years are equally distributed in the pockets of America, then pre-1965 “silver” coins would comprise ~20% of the samples, and the average mass of (for example) a dime would shift up from 2.27 grams to 2.32 grams – about a 2% weight gain. The penny is a more severe case; an even distribution over the last fifty years would yield an almost 50/50 distribution of heavier (3.1g) pennies, making the average penny weigh 2.8g, a 12% error. Quarters went from 6.25 grams down to 5.67 grams in 1965, so even distribution would yield about a 2% gain in mass. The mass of the nickel remained unchanged.
The effects of such a sample would be interesting; the sheer volume of pre-1982 pennies along with minor contributions from dimes and quarters would mean that a large sample would be almost 6% heavier than the same distribution of all-modern coins. Once you add in their relative values**, it turns out that my hypothetical 50-year “perfect” sample of coins (galt’s distribution) is worth about 5% less by mass: about $26.73 per kilogram. An evenly-distributed twenty-year sample would be much closer to expectations; “silver” coins would have constant mass and pennies would add less than 1% phantom mass (that is, a change of mass with no corresponding change in value). As a curiosity, a sample of coins that were all from before 1965 would be worth $24.64 per kilogram – a 12.5% drop in value (by mass)!
I really doubt we’ll see an even distribution out there; in fact, I suspect that coins have a “half life” and that as time goes on, fewer and fewer coins from each year are available. Mint production volume also fluctuates: in the last 3 years the number of pennies produced annually varied from 6.1 billion (2006) to 7.7 billion (2005) with 2004 coming in between with 6.8 billion. Other coin production varied similarly. I’m sure somebody out there knows how the coin years are distributed within the set of circulating coins, but if they do, they know it from sampling. If you’re aiming for accuracy, and you know that the coin sample contains pre-1982 coins, then you should probably shave your value estimate down by maybe one percent, at most.
So now we know that the presence of older coins hurts our ability to estimate value by mass alone. Unless we can predict the packing factor for flat cylinders in mostly-cylindrical containers, we can’t estimate by volume alone except to determine an upper bound. But both estimates together, taken with an assumption of the distribution of change in circulation, can give solid upper and lower bounds for the value of a known mass/volume of coins.
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- the circulated half dollar retained its silver content until 1970, but is almost never seen in circulation.
** - and ignore the possibility that you’ve got an ultra-rare coin worth $300 in your coin jar. 
