The simple and honest answer is no, you can’t make espresso or cappuccino with a single serve coffee maker.
The heat of the water, and pressure applied, have a very specific action on the coffee grinds. The chemical process that takes place is different from that which can be achieved with gravity fed water.
In other words, to make espresso, you have to use an espresso machine. Neither regular coffee brewers nor single serve coffee makers can apply that kind of pressure to the water.
That said, some one cup brewers can make you a passable “faux espresso” or cappuccino.
The Senseo brewers use a patented “frothing chamber” to give you a kind of crema on the top of your coffee.
And the Tassimo Hot Beverage System actually has two disc holders – one for coffee and one for milk. The resulting brew has the appearance of a cappuccino and will likely satisfy coffee lovers who like a frothy, milky coffee.
But even with the Tassimo, it’s not a real cappuccino, and the base brew is not a real espresso.
If you want to make espresso with the simplicity and convenience of a single serve machine, you can check out the various Nespresso machines.
Nespresso makes espresso makers which use single-serve cups, much like the Keurig K-Cups or Tassimo T-Discs.
But keep in mind, these machines are designed to make espresso, and can’t be used to brew regular coffee.
The Keurig B60
The Senseo SL7810
The Tassimo Hot Beverage System