Не тестировал.
$('.cart__goods_item').find('.cart__numbers_plus,.cart__numbers_minus').on('click',function(){
var $t=$(this),
$item=$t.parents('.cart__goods_item'),
$res=$item.find('.cart__numbers_result'),
value=parseInt($res.text());
if($t.hasClass('cart__numbers_plus'))
value++;
else
value--;
$res.text(value<1?1:(value>10?10:value));
});
$('.cart__goods_item .cart__numbers_reload').click(function(){
$('.cart__goods_item .cart__numbers_result').text(1);
});