First, you may consider signing up for a free 30-day trial if you don't already have Amazon Prime. If you don't utilize the service during the trial, simply avoid renewing.
If you already have the service or want to sign up for the first time, you can lock in the current price of $119/year. All you need to do is purchase a "Gift of Prime" membership for yourself, which essentially allows you to buy a one year Amazon Prime membership at the current rate. After you've done this, set your subscription to not auto-renew. Once your membership expires, you can apply your purchased one year membership to your account. You can purchase multiple Gift of Prime memberships and lock in the lower rate for years to come.
If you're looking for a completely free Prime membership, select Metro by T-Mobile cell service plans give complimentary access to Prime.
Lastly, if you're sure you want Amazon Prime, it may be advantageous to sign up for the Amazon Prime Rewards Visa Signature Card. The card comes with an instant $100 gift card upon approval, however, you must already have Amazon Prime prior to applying. So the gift card would be more of a way to offset the cost of the subscription.