If the Day Care lady says that your two Pokemon don't like playing together, then it means your two Pokemon will never breed. If it is true you have deposited two Charmander, the only way you can receive this message is if they are the same gender. Double-check the Pokemon are of opposite sexes, as you've almost certainly mistaken this.
Assuming you've got two males (as per the 87.5% gender ratio), you'd need to trade in a female or find a Ditto if you want to breed a Charmander. If you've reached the second island, Ditto should be easy to access by completing the Ditto Five sidequest, assuming you're playing US/UM.
