We address the problem of cooperative manipulation of an object whose tasks are specified by a Signal Temporal Logic (STL) formula. We employ the Prescribed Performance Control (PPC) methodology to guarantee predefined transient and steady-state performance on the object trajectory in order to satisfy the STL formula. More specifically, we first provide a way that translates the problem of satisfaction of an STL task to the problem of state evolution within a user-defined time-varying funnel. We then design a control strategy for the robotic agents that guarantees compliance with this funnel. The control strategy is decentralized, in the sense that each agent calculates its own control signal, and does not use any information on the agents' and object's dynamic terms, which are assumed to be unknown. We experimentally verify the results on two manipulator arms, cooperatively working to manipulate an object based on a STL formula.