Climate Stewardship Act of 2019 This bill provides funding and incentives for states, Indian tribes, local governments, and other entities to carry out climate stewardship practices, including farm and ranch conservation practices, reforestation projects, and wetland restoration projects. For example, the bill extends through FY2030 the Conservation Reserve Program, the Agricultural Conservation Easement Program, the Environmental Quality Incentives Program, and the Conservation Stewardship Program. It also modifies and increases funding levels for some of these programs. The Forest Service must award cost-share grants to states, Indian tribes, local governments, and nonprofit entities to conduct projects to reforest certain land. The bill also establishes a civilian conservation corps to provide youth from low-income communities, indigenous communities, and communities of color with the academic, vocational, and social skills necessary to pursue long-term, productive careers in the forest sector and the wetland restoration sector. Further, the bill sets forth a grant program for states, Indian tribes, local governments, institutions of higher education, and nonprofit entities to conduct coastal wetland restoration projects, including projects that mitigate greenhouse gas emissions.