This isn't the most elegant solution, but it is a quick fix. In templates/orderforms/standard_cart/addons.tpl you can set the billing cycle for each addon if you know the addon ID:
<div class="product-pricing">
{if $addon.free}
{$LANG.orderfree}
{elseif $addon.id == 1}
<span class="price">{$addon.recurringamount} Annually</span>
{if $addon.setupfee}<br />+ {$addon.setupfee} {$LANG.ordersetupfee}{/if}
{elseif $addon.id == 2}
<span class="price">{$addon.recurringamount} Monthly</span>
{if $addon.setupfee}<br />+ {$addon.setupfee} {$LANG.ordersetupfee}{/if}
{else}
<span class="price">{$addon.recurringamount} {$addon.billingcycle}</span>
{if $addon.setupfee}<br />+ {$addon.setupfee} {$LANG.ordersetupfee}{/if}
{/if}
</div>
