A 2'x2' cage is too small even for a single adult dragon, so deffinitely too small for a pair. The minimum sized cage for a single adult should have a floor space of 2'x4'. The best thing you should do is build or buy two cages that are 2'x4'x2' (though the height can be as low as 16", floor space is important for dragons though some height is good as they are semi-arboreal).
Though two adult dragons can be housed together, and since you have a male and female pair, it would be better to house separately, unless you want to have lots of babies and risk stress on teh female due to repeated mating attempts by the male. The smaller cage can be used for some hatchlings, though you will need to get many more (10-20gal tanks are good for 1-5 hatchlings each).
If you plan on incubating the eggs from the female once she lays, you will need to buy an incubator or build one. You will need to incubate the eggs at around 85F. Female dragons can lay up to 30 eggs per clutch and have several clutches per breeding season, usually about 3-4 weeks apart. Make sure she gets extra calcium and protein to help with egg laying. The other poster described pretty well what you need to do to produce an egg laying bin.
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PHLdyPayne