Influence of cosmological constant on toroidal fluid configurations around charged spherically symmetric black holes and naked singularities is demostrated by study of perfect fluid tori with uniform distribution of specific angular momentum orbiting inthe Reissner-Nordstrom-(anti-)de Sitter spacetimes. Toroidal configurations are allowed only in the space times admitting existence of stable circular geodesics. Configurations with marginally closed equipotential (equipressure) surfaces crossing itselfin a cusp allow accretion (through the inner cusp) and/or excretion (through the outer cusp) of matter from the toroidal configuration. Detailed classification of the Reissner-Nordstrom-(anti-)de Sitter spacetimes according to properties of the marginally stable tori is given. It is demonstrated that in the Reissner-Nordstrom-de Sitter naked-singularity spacetimes an interesting phenomenon of doubled tori can exist enabling exchange of matter between two tori in both inward and outward d