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.