Is it permissible to delay paying the price of gold and the cost of having it made into jewellery?

What we understand from the question is that you are going to
buy the gold from this craftsman, and he will make it into jewellery. If
that is the case, it is not permissible, rather what you should do is pay
the price of the gold (in cash) and take possession of the gold in one
sitting. As for the cost of making it into jewellery, it is permissible to
delay it. 

But if what is meant in the question is that you are going to
give the craftsman gold that you already own, so that he can make it into
jewellery, then there is nothing wrong with delaying payment. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: 

It is proven that the Prophet (peace and blessings of
Allaah be upon him) said: “Gold for gold, silver for silver, wheat for
wheat, barley for barley, dates for dates, salt for salt, like for like,
same for same, hand to hand.” 

And it is proven that he (peace and blessings of Allaah
be upon him) said: “Whoever gives more or asks for more has engaged in
riba.”  

And it is proven that he (peace and blessings of Allaah
be upon him) was brought some good-quality dates. He asked about them and
they said: “We used to take one saa’ for two saa’s, and two saa’s for
three.” The Prophet (peace and blessings of Allaah be upon him) ordered
that the transaction be cancelled and he said, “This is the essence of
riba.” Then he told them to sell the inferior dates and to buy good-quality
dates with the dirhams. 

From these ahaadeeth we may understand that what the
questioner said about exchanging gold for gold and adding the cost of making
one of them into jewellery is something that is forbidden and is not
permissible. It comes under the heading of riba which the Prophet
(peace and blessings of Allaah be upon him) forbade. The correct way to do
it is to sell the broken gold for a certain price without any other
conditions. After the seller has taken the price, he may then buy the new
gold. It is better to look for the new gold in another place, and if he
cannot find it then he may return to the one who bought from him, and buy it
with dirhams. If it costs more it does not matter. What matters is that
there should not be an exchange of gold for gold with an extra payment, even
if that is for making it into jewellery. 

This applies if the seller is a merchant. If the merchant is
also a goldsmith he can say: “Take this gold and make it into jewellery for
me (whatever he wants him to make), and I will pay you for that when you
finish making it.” There is nothing wrong with this. End quote. 

Majmoo’ As’ilah fi Bay’ wa Shira’ al-Dhahab
(no. 1). 

The Shaykh was also asked: 

Is it essential to pay for work when collecting the gold (to
the goldsmith) or can we regard it as an ongoing transaction? 

He replied: 

It does not have to be
paid up front, because this is payment for work. End quote. 

Majmoo’ As’ilah fi Bay’ wa Shira’ al-Dhahab
(no. 10).  

And Allaah knows best.