We have analyzed and measured the quantum coherent dynamics of a circuit containing two-coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two qubits are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation of the qubit circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each qubit by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup, the measured pulse-induced probe currents are proportional to the probability for each qubit to have an extra Cooper pair after the manipulation. As expected from theory and observed experimentally, the measured pulse-induced current in each probe has two frequency components whose position on the frequency axis can be externally controlled. This is a result of the inter-qubit coupling which is also responsible for the avoided level crossing that we observed in the qubits’ spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape, the system remains entangled most of the time reaching maximally entangled states at certain instances.