How do I create spherical coffee?
I would try the cold oil spherefication method. Using agar agar as your gelling agent. The cold oil spherefication involves a solution which is in this case coffee that contains 1% to 2% agar (depending on desired consistency). The solution, which is warm is then inserted into a cold oil bath. Which will set the agar.

Why agar? Because agar melt at 85C. Making it perfect if your serving it in a latte. 

You'll have to start by chilling your oil in bowl in the freezer for about 30 minutes. Lets say 1 litre. Next measure the amount of coffee your gelling and add your agar ( i would start with 1.5%) so for 100ml 1.5g agar. Bring this solution to a boil in a pan. Agar disolves at 95C. Keep wisking because if will catch. You'll see a change in viscosity, then you know your there. 

Now there is alot of ways adding the droplets to your oil bath. Syringes and pipettes and so on. My recomendation is to use a squeezy bottle with a tin nozzle. Take your bowl of chilled oil and spin it ( i guess the choice of bowl and surface is of essence here). A round bottom bowl on an ice bath would be ideal. Now, gradually in a neat stream start dripping with your squeezy bottle into the side of the bowl. And there you are, Agar gellies!