Conservation for Very Erodible Row Cropland Act of 2018 or the COVER Act This bill amends the Food Security Act of 1985 to modify Department of Agriculture (USDA) conservation programs to authorize additional assistance for farm practices related to soil health and carbon storage. The bill modifies the Environmental Quality Incentives Program to require USDA to provide payments under the program for practices that: improve soil health, enhance the ability of a farmer to absorb and recover from shocks and stresses to production, increase the storage of carbon on agricultural land, and achieve other conservation outcomes determined by USDA. The bill modifies the Conservation Innovation Grants program to establish a pilot program to provide payments to encourage: (1) the measurement of outcomes relating to the planting of a regionally appropriate cover crop, and (2) opportunities to increase farm income. In carrying out the program, USDA must prioritize certain projects with third-party partners such as academic entities, carbon offset protocol developers, livestock producers, and food manufacturers.