These stories are known and loved by millions of people all around the world. They would make an amazing set with each of the stamps telling their own story:

1) Aladdin and the Wonderful Lamp

Luckily for us, Disney doesn't own this tale. Stamp with the Jinn (Genie) would be perfect.

2) Ali Baba and the Forty Thieves

I guess everyone knows the plot, so I was thinking something with the treasures and the cave, but there other options as well

3) Sinbad the Sailor

There are many ideas and many creatures/monsters here, because Sinbad traveled near and far. I was thinking about something with the giant bird, but there's a lot to choose from.

4) Scheherazade

The main storyteller, who outsmarted the murderous sultan and stayed alive by telling him stories every night withouth finishing them

5) Prince Ahmad and the Fairy Peri-Banu

Peri can be decribed as a female jinn. Integral to the Persian mythology, and also present in the tales from 1001 nights. I think another stamp with a female character is needed, and this one would be perfect.

6) Magic Carpet

Not exclusive to Arabian Nights, but it's hard to imagine the set without it. Within the same tale, Prince Hussain, the eldest son of the Sultan of the Indies, travels to Bisnagar (Vijayanagara) in India and buys a magic teleporting tapestry, also known as a magic carpet.