Adapter for a rolling assembly, the said rolling assembly having an axis of rotation and comprising a tyre having two beads, a rim having two rim bead seats, the said adapter providing the connection between one of the beads and the rim, the said adapter comprising: - an axially inner end intended to be mounted on a rim bead seat and comprising an inner reinforcing element and a substantially radial axially outer face; - an axially outer end intended to come into contact with a bead and comprising an outer reinforcing element and a substantially radial axially inner face or bearing face; - a substantially axial body connecting the said axially outer end to the said axially inner end so as to form a single piece; - the said body comprising an adapter seat intended to receive the bead and situated near the axially outer end; - the said body comprising at least one main reinforcement providing the connection between the outer reinforcing element and the inner reinforcing element, the main reinforcement comprising at least one first and one second reinforcing ply which are placed radially relative to one another, the said reinforcing plies (18, 19) each comprising mutually parallel reinforcers coated in elastomer composition referred to as skim rubber; - characterized in that a layer of elastomer composition in a colour other than black, also referred to as coloured rubber, is positioned, as desired: - in place of the skim rubber with which the reinforcers of each ply are coated, or - in place of the skim rubber with which the reinforcers are coated and placed only on the exterior periphery of the reinforcing plies, or - on the outside of the skim rubber. - an axially inner end intended to be mounted on a rim bead seat and comprising an inner reinforcing element and a substantially radial axially outer face; - an axially outer end intended to come into contact with a bead and comprising an outer reinforcing element and a substantially radial axially inner face or bearing face; - a substantially axial body connecting the said axially outer end to the said axially inner end so as to form a single piece; - the said body comprising an adapter seat intended to receive the bead and situated near the axially outer end; - the said body comprising at least one main reinforcement providing the connection between the outer reinforcing element and the inner reinforcing element, the main reinforcement comprising at least one first and one second reinforcing ply which are placed radially relative to one another, the said reinforcing plies (18, 19) each comprising mutually parallel reinforcers coated in elastomer composition referred to as skim rubber; - characterized in that a layer of elastomer composition in a colour other than black, also referred to as coloured rubber, is positioned, as desired: - in place of the skim rubber with which the reinforcers of each ply are coated, or - in place of the skim rubber with which the reinforcers are coated and placed only on the exterior periphery of the reinforcing plies, or - on the outside of the skim rubber. - in place of the skim rubber with which the reinforcers of each ply are coated, or - in place of the skim rubber with which the reinforcers are coated and placed only on the exterior periphery of the reinforcing plies, or - on the outside of the skim rubber.