Pandas number rows within group in increasing order

Use groupby/cumcount:

In [25]: df['C'] = df.groupby(['A','B']).cumcount()+1; df
Out[25]: 
   A  B  C
0  A  a  1
1  A  a  2
2  A  b  1
3  B  a  1
4  B  a  2
5  B  a  3

Use groupby.rank function. Here the working example.

df = pd.DataFrame({'C1':['a', 'a', 'a', 'b', 'b'], 'C2': [1, 2, 3, 4, 5]})
df

C1 C2
a  1
a  2
a  3
b  4
b  5

df["RANK"] = df.groupby("C1")["C2"].rank(method="first", ascending=True)
df

C1 C2 RANK
a  1  1
a  2  2
a  3  3
b  4  1
b  5  2