A good thumb: is the "couple" a single unit of apples? Or is it a number of apples? Generally, "a couple" [as in "a few"] represents a number.
Here, when you say "there are a couple of apples," you are really saying:
There are two apples
Hence the plural "are" is correct. However, consider the following:
A pair of aces is the best hand in Texas Hold'em.
To reiterate: the decision is based on whether the subject of the sentence is a singular or plural noun. It does NOT matter whether the noun refers to one or many things. A couple [of items] is a plural noun. A pair is a singular noun. Unfortunately, as far as I can tell this needs to be memorized case-by-case.
My pants are blue
My pair of pants is blue
The newborn twins are happy
The kids are happy
The parents are happy
The whole family is happy
The married couple is happy
A pair, a family, and a married couple are all single objects. "Twins" refers to a group of people.
The twins are happy
The Republicans are happy
The human race is happy (The human race is not a group of people, it's rather a single race, as opposed to the Martian race or the Dolphin species.)
Again, all that matters is "what term is the subject of the current sentence?", no matter what the term refers to.
That married couple? I hope they are happy. ("They" is the subject of the second sentence, which is a plural noun.)
The twins are very troublesome.
The twins? That pair is very troublesome. ("That pair" is a singular noun.)
The twins are a troublesome pair. ("The twins" is the subject - it doesn't matter that the subject describes a single pair.)