Well, it's like a game of Blackjack: to know the answer for sure, you'd have to bust your speakers.
If you have any amplifier at home or that you can borrow for a while, connect the speakers, put some music on WITH VOLUME SET A ZERO, and VERY CAREFULLY, turn up the volume litlle by little to see (actually to hear) how the speakers behave. Unless the amp is of much lower power than the speakers can stand, there will be a point where the volume you hear will be appreciable and the sound will be clear and defined (depending, of course, on the quality of amp and speakers). You can try (at your own risk) to push the volume further up a little bit, untill you hear occasional distortion and buzz from the speakers. Then you'll know you've overcome the maximum advisable power.
Depending on the position of the volume knob, you'll have a sort of relationship with the power of the amp (as a simple approximation, use a proportional relationship).
An additional previous step is to measure the impedance of the speakers with a multimeter. Set the multimeter to resistance measuring and measure the resistance of each speaker. Do it for both speakers to compare results. If one or both of the speakers measure 0 or infinite resistance, then it's busted, and you don't need to loose any more time. Otherwise if all is well it should give a measurement of approximately either 4 or 8 ohm (as almost virtually any commercially available speaker has one of these two values of impedance).
That's an important characteristic (as important as rated power) and it's one you can actually measure, so it's worth spending 5$ on a simple multimeter if you don't have one.
Once you know the speakers impedance, do the power testing with an amp with the same output impedance (if you can) and buy one with the same output impedance.