Here is how I do this on my 1.9.2.2 Website : (I think it must be the same solution as @barry-carlyon, but I will detail mine)
First, I give an id (form-update-post) to the form of the cart page : (checkout/cart.phtml)
<form action="<?php echo $this->getFormActionUrl() ?>" method="post" id="form-update-post">
Then, I add two buttons, and I add an id to the qty field of the items : (checkout/cart/item/default.phtml)
<a href="javascript:decreaseQty(<?php echo $_item->getId() ?>)" class="decrement_qty"><span class="fa fa-minus"></span></a>
<input id="quantity-item-<?php echo $_item->getId() ?>" name="cart[<?php echo $_item->getId() ?>][qty]"
data-cart-item-id="<?php echo $this->jsQuoteEscape($_item->getSku()) ?>"
value="<?php echo $this->getQty() ?>" size="4" title="<?php echo $this->__('Qty') ?>" class="input-text qty" maxlength="12" />
<a href="javascript:increaseQty(<?php echo $_item->getId() ?>)" class="increment_qty"><span class="fa fa-plus"></span></a>
Notice that the link of the buttons are javascript functions : (javascript:increaseQty, javascript:decreaseQty)
The last step is to add those Javascript functions in the cart page : (checkout/cart.phtml)
<script type="text/javascript">
function increaseQty(id){
var input = jQuery("#quantity-item-"+id);
input.val(parseInt(input.val())+1);
var form = jQuery("#form-update-post");
if(form !== undefined){
form.submit();
}
}
function decreaseQty(id){
var input = jQuery("#quantity-item-"+id);
if(input.val() > 1){
input.val(input.val()-1);
}
var form = jQuery("#form-update-post");
if(form !== undefined){
form.submit();
}
}
</script>
What it is doing is increasing or decreasing by one the field of the quantity for the given item, then submitting the form of the cart. This way, the page will reload, and the new quantity will be saved.