You can also make dua after the tashahud but before the salam. There are several specific duas that can be recited after the tashahud. The one I usually recite is:
Allahuma inna a'udzubika min a'zabi jahannam, wa min a'zabil kubri, wa min fitnatil mahya wa mamati, wa min fitnahtil masihi dajjal
(O Allah, I seek your protection from the tortures of Hell, from the tortures of the grave, from the trials of life and death and the trials of the false messiah (Ad-dajjal))