I am going ot buy my cousin a cd

voy a comprar mi primero un cd

is my translation correct

That looks good.

With an indirect object (my cousin) in Spanish it is always best to include the indirect-object pronoun. Because you are using "ir + a + infinitive" you have a choice between 2 positions:

a) Le voy a comprar a mi primo un disco compacto.

b) Voy a comprarle a mi primo un disco compacto.

NOTE: Try not to confuse "primero" = first with "primo" = cousin and don't forget the "a" we discussed in an earlier post!

Sra

Well almost. you are on the right track but here let me help:

Yo voy a comprar un cd para mi primo.
I am going to buy a cd for my cousin.

Your translation is almost correct, but there is a small mistake. The correct translation of "I am going to buy my cousin a CD" in Spanish would be:

"Voy a comprarle un CD a mi primo/a."

The word "primo" is used for "cousin" in Spanish. Additionally, you need to use the indirect object pronoun "le" before the direct object pronoun "un CD" to indicate that you are buying the CD for your cousin.