We consider two options for improved design of the beryllium target as part of the target–moderator–reflector assembly of the Compact Neutron Source DARIA. The neutronics and thermal calculations of the target assembly are made in order to select its optimal geometric characteristics. Spatial-energy distributions of the fast neutrons are presented. Based on the calculations of the neutron yield, we have chosen the position of the Bragg peak of the protons, the optimal thickness and diameter of the cylindrical target. We discuss two options for target cooling in the water and in the air as well.