"the largest amount of money in coins without being able to make change for a dollar "


ANY number of coins of larger denomination than one dollar would still leave you unable to make change for a dollar.

The listed denominations greater than one dollar would be available in unlimited number, ( if one had the means) thus one could have a large amount, in coins, and still be unable to make change.

The given figure of $1.19 is still incorrect, as the addition of a half-cent would STILL leave one unable to make change for the dollar.
Or, instead of the four pennies, use 4 three cent pieces...