There is a rank
function to help you with that:
transform(df,
year.rank = ave(count, year,
FUN = function(x) rank(-x, ties.method = "first")))
item year count year.rank
1 a 2010 1 3
2 b 2010 4 2
3 c 2010 6 1
4 a 2011 3 2
5 b 2011 8 1
6 c 2011 3 3
7 a 2012 5 3
8 b 2012 7 2
9 c 2012 9 1