Discount codes are the most straightforward way to offer a temporary promotion for both new and existing customers. New customers enter the discount code at checkout and you have the option to apply a discount to an existing subscription manually or by applying discount codes in bulk. 

You can also adjust the price of your products and re-adjust pricing once the promotional period is over. Note that if you use subscribe and save rules, the subscription discount is calculated on the discounted price.

Workflows could also be used to automate the price change back to the regular recurring price. 

Bundles are also an option for Pro merchants on Recharge Checkout on Shopify and the Shopify Checkout Integration. Bundles offer a "build-a-box" experience that can include specific products bundled at a fixed price and offered at a quantity discount.