Question

Can they make a egg in the day care centre if theymr different genders and different Pokemon

Answer 1

Yeah.

So long as they are opposite genders and have a matching Egg Group, they can breed.
The Species and type do not matter.

Answer 2

Yes, it is possible to breed Pokemon that are different genders as long as they are in the same egg group. Also, if you put a ditto (which is genderless) in the daycare, it should breed with most Pokemon.

If you want to find out more about egg groups:bulbapedia.bulbagarden.net/wiki/Egg_groups

I hope this was helpful!