Look in the clock and see if you can see and remove the crystal. They're usually 32.768 kHz. That frequency is an integer power of two so it's easy to generate a 1 s clock by division $ \frac {32768}{2^{15}} = 1 $.

Have a look in the electronics catalogues for crystals with the relative frequency you require and try them out. If you're lucky the oscillator may be able to lock in on the new crystal frequency.