When the Daycare man says "they don't seem to get along" it doesn't mean they can't breed. It actually means they can breed.
If he says that "they prefer to play with the other Pokemon" then it means that they are unable to breed at all.
He will say "they don't seem to get along" when you are trying to breed 2 Pokemon in the same egg group (or with a Ditto), but are different species and have the same Trainer ID number. When this is the case the Pokemon have around a 20% chance of giving you an egg every 255 steps you take. You can increase this chance by breeding Pokemon of the same species (different genders, obviously). This is not always possible, however. The other way to increase the chance of getting an egg is to have one of the Pokemon from a different trainer (and so has a different ID number).