Interesting challenge. Basically, you are asking for a RANKIF formula.

I'm sure it can be done in a single formula and I found some possibilities (using SUMPRODUCT etc) that I don't have energy to work out tonight.

An easy solution I can come up with right now is to have a helper column.

So, in column D put this formula:

=IF($A$2>A2,"",C2)

Then, in column E, put this one:

=IF(ISNUMBER(D2),RANK(D2,$D$2:$D$11,0),"")

If that doesn't work for you, then I might have more time tomorrow night.