We study the alpha-effect associated with exponentially growing perturbations of the Euler flow with elliptical streamlines in a rotating frame, in the presence of a uniform, external magnetic field perpendicular to the plane of the flow. The fluid is perfectly conducting. We are motivated by the problem of possibility of dynamo action triggered by tidal deformations of astrophysical objects, such as stars, planets and accretion disks. The ellipticity of the flow models therefore the tidal deformations in the simplest way. By the use of the analytical technique developed by Lebovitz & Zweibel 2004, in the limit of small elliptical (tidal) deformations, we find resonant growing modes and calculate their group velocities, helicities and alpha coefficients. The case of mixed-resonance, between hydrodynamic and magnetic modes, leeds to non-zero alpha coefficient, even when no dissipation is present. Because the analysed modes are unstable, the coefficient alpha grows exponentially in time, leading to a double exponential growth of the mean field. Motivated by astrophysical applications, we also find that the results obtained apply exactly to short-wavelength perturbations of Riemann ellipsoids, penetrated by a uniform magnetic field.