Use Build Array to append to an existing array. After placing Build Array on your diagram, add an input to it (just stretch it with the mouse or right click and select Add Input). Wire the top input to your existing array and the bottom input to the string you want to add to the array. In labView 6.1, the top input in Build Array will automatically change to an array input. In LabView 5.1 or older, you have to right click on the input and select Change to array (or some words to that effect).
See the attached LabView 6.1 example.