I am afraid I have no experience in creating an aviary but I did some research for you and below are some blueprints and tips on how to do it. I don’t think you will “need” a large cage as lovebirds are small birds. However, I think that they will love the opportunity to fly around and be birds. You must love your pets very much:)

In terms of materials, just keep in mind that some woods are not got for birds and birds tend to chew. So do your research and find a compatible wood type for your cage. Also I suggest linoleum floors that are easy to clean and water proof. Also you will need some mesh and if you can, make sure its made of stainless steal as metal containing nickel and other heavy metals can hurt a bird if your birds are one of the birds that like to chew metal. (Mine loves metal and hates all other “soft” toys). In terms of costs, I am not sure. If you are very skilled, you own your own tools already mand you don’t make the cage huge, I think probably 200 dollars (not including plants and toys you might want to add). If you can section of a part of a wall I think that will reduce costs as you don’t need to create all the four corners/walls. However if you want to include lamps and such that might bring the cost up more. Just keep in mind that the birds might land on the lamps and chew on cords and even birn themselves on the lamp.

Also please refrain from using glass unless it is brown or dark on their side as birds tend to fly into glass.

Anyways I hope this helped.
Good luck!!!

Regards
Anna