You say that your call to getJSON is returning "views" which has a single string as its value:
"[2, 2, 61]"
However, when you change the code to:
var values = [2, 2, 61];
In this case you are correctly specifying an array of three integers.
Change your method which returns the JSON so that it correctly returns and array of integers for "views" instead of a single string i.e.
{"screen" : "1220x1080, 1620x1080, 1920x1080", "views": [2, 2, 61] }
See the jsFiddle here.
Also you say that your call to $.getJSON is working, but the method call you have written is not normal. See here for jQuery's getJSON documentation.
The following should work:
var values;
$.getJSON( "models/ucp/traffic/traffic_display_bos.php", function(data) {
values = data.views;
});
$('#traffic_bos_ss').sparkline(values,
{
type: "pie",
height: "100%",
tooltipFormat: 'data.screen - {{value}}'
});