Shared code in blockchains, known as smart contracts , stands to replace important parts of our digital governance and financial infrastructure. The permissionless execution of smart contracts is tightly coupled to cryptocurrencies and Proof-of-Work blockchains. As a result, smart contracts inherit the environmental impact of Proof-of-Work blockchains, such as its energy consumption, carbon footprint, and electronic waste. The four concepts of relaxed consistency, strong identities, probabilistic consensus, and the use of liabilities instead of assets may change the status quo. This work explores the integration of these concepts to decouple smart contracts from Proof-of-Work blockchains. By means of a local-first approach, which may expose users to inconsistent ephemeral contract states, the architecture of smart contracts can be transformed to become green. Because such contract states may be dropped, we base the interactions between users on liabilities. We propose a novel paradigm for smart contract architectures, named Green Smart Contracts, that is based on a local-first approach. Furthermore, we present and implement a prototype solution for this paradigm. We validate the need for a mechanism to resolve consistency violations by replaying the contract calls of a real smart contract. Our simulation shows that violations occur more often (13% of contract invocations) when using liabilities than when using a traditional blockchain (3% of contract invocations). However, we additionally validate that they can be avoided using a consensus mechanism, and our experiments show that a publish-subscribe messaging pattern uses the fewest messages to do so, though it may not be applicable for use cases that disallow the inherent imbalance in the messaging between peers. Our carbon emission estimation shows that a Green Smart Contract approach lowers carbon emissions by 52.31% when compared with the messaging behavior of a typical peer-to-peer blockchain with 1000 nodes.