This dragon breeder is designed for just that! Dragon breeding!

You can even use it for any non-alpha dragon in DragonForge!
First, you will need these materials:

Build up a nice 3 block tall pillar. Then two more so that they form a wall. Now make a roof with the remaining stone or other fire-proof material. Make the floor out of hoppers, all connecting to each other, except the two middle ones. Next, dig two blocks down from where the hoppers are, & hollow out that space. place two stone in the two middle spaces. & then a double chest on top of those.
Really taking shape, huh?
Make stairs down to the hollowed pit. & finally, put up a fence. As well as trap doors on the stair case. If you want, you could put in a gate, so that you can swap dragons. Just spam-click* on the male dragon, & the chest will fill up with the Female’s Eggs.
(* But please, no spam, OK?)