There ARE dollar coins, so you can't have one of those! So technically
you can't have 99 cents with at least one of EVERY coin. Half dollars are
not in circulation, but they exist and can be bought from the US mint, but
only coin collectors ever buy them. I'll assume you mean every coin less
than a dollar coin.
If you had 1 of each of the 5 US coins, you'd have 50+25+10+5+1 = 91 cents.
So then you'd need to make 8 more cents with 4 more coins. You can do that
with 1 more nickel and 3 more pennies.
Answer: 1 half dollar, 1 quarter, 1 dime, 2 nickels, and 4 pennies.
Edwin