Besides calling .ajax() instead of .getJSON() as Darin suggests or setting the global jQuery.ajaxSettings.traditional to true as jrduncans suggests, you can also pass the result of calling the jQuery .param() function on your params object:

var id = [];
var inStock = [];

$table.find('tbody>tr').each(function() {
    id.push($(this).find('.id').text());
    inStock.push($(this).find('.stocked').attr('checked'));
});

var params = {};
params.ids = id;
params.stocked = inStock; 

$.getJSON('MyApp/UpdateStockList', $.param(params), function() {
    alert('finished');
});    

Besides calling .ajax() instead of .getJSON() as Darin suggests or setting the global jQuery.ajaxSettings.traditional to true as jrduncans suggests, you can also pass the result of calling the jQuery .param() function on your params object:

var id = [];
var inStock = [];

$table.find('tbody>tr').each(function() {
    id.push($(this).find('.id').text());
    inStock.push($(this).find('.stocked').attr('checked'));
});

var params = {};
params.ids = id;
params.stocked = inStock; 

$.getJSON('MyApp/UpdateStockList', $.param(params, true), function() {
    alert('finished');
});