If his relatives want particular types of perfume, is it permissible for him to buy them and sell them to them?

If they know that you are going to buy it then sell to them and make a profit from them, there is nothing wrong with that. But you should not sell anything to them until you buy it and take possession of it first, because of the report narrated by al-Nasaa’i (4613), Abu Dawood (3503) and al-Tirmidhi (1232) from Hakeem ibn Hizaam who said: I asked the Prophet (blessings and peace of Allah be upon him): O Messenger of Allaah, people come to me wanting to buy something that I do not possess; should I buy it for them from the marketplace? He said: “Do not sell that which you do not possess.” 

This hadeeth was clased as saheeh by al-Albaani in Saheeh al-Nasaa’i. 

You do not have the right to do a deal with them until you buy the product first, and take possession of it yourself. 

But if you are just acting on their behalf to buy something for them, then you do not have the right to add anything to the price of the goods; rather anything that you get in the process, such as gifts or discounts, should go back to them, because the one who is acting on someone’s behalf has been entrusted with something and any gain or profit he makes should go back to the one who delegated him. See question no. 36573. 

If you want to make money from them, then tell them that you can sell a certain type of perfume to them for 45 or 50, or ask about the kind that they want, then tell them the price. If they want to buy it, you can buy it and sell it to them, and you do not have to tell them about the price for which you bought it, but they should understand that you are a seller and not acting on their behalf, as discussed above. 

And Allah knows best.