'Couple' can mean two. In fact, it always means 'two' if you are talking about a relationship. For example, "Mike and Anna are a couple." and is mostly used for things that are pairs.
BUT it is often used informally to mean an indefinite small amount. For example, "Sorry, can't talk for long, I only have a couple of minutes." In this case the person does not specify the exact amount of time, just that it is a short amount of time. Could be two, three, four or ten minutes! Depends what the person thinks is a small time.
'a handful' can mean the amount you can hold in your hand. BUT everyone's hand is different, so again there is no specific definite amount. HOWEVER, it is worth noting that 'a handful' often carries a nuance of meaning because it means 'not many'. If you say "a handful of researchers" it can imply 'not enough' or 'there is a need for more researchers'.