Surface Mount Springs, how are they called?
Mill-Max (mill-max.com) makes a huge variety of spring-loaded contacts, some forms of which are commonly known as "pogo pins". They come in a variety of shapes, sizes, spring travel, and (most important) shape of the contact end of the pin.  Digikey carries a lot of them.

You'll also need some kind of jig to hold the part under test firmly against the contacts, but presumably you already know this.