Young Link can pick up the second bottle in Kakariko Village. Go over to the lady standing by the chicken pen. She will tell you that her cuccos have ran away and she wants you to bring them back to the pen. There are 7 cuccos scattered throughout the village. Every time you enter a house or leave the village, they'll all escape the pen again, so you'll have to do it in one shot. Here are the locations:
After you bring all 7 cuccos back the lady will give you an empty bottle for your work and explain that although she loves cuccos she couldn't get them herself because she's allergic to them and gets goose bumps.