I don't want my guys to breed ( in case they are male/female)....and you might want to double think that....babies are a huge responsibility and if your guys are young, they may not know how to behave as parents and it can fall on your shoulders to hand feed.
Frankly, I also don't want to try and find homes for babies and I figure that it won't just happen once...it'll happen again and again and again.
What I do when they start to shred is just let them but I clean it up often. I DO NOT provide a nesting box. Now, to be honest, I have heard that if you don't want them to breed, you shouldn't provide shredding material but when I tried that, they started to line the "nest"( the cage bottom) with their OWN feathers so I didn't think that was a good thing at all. As for the nesting box, believe me, they don't need it to try and find a place to lay. I've had eggs in the weirdest places...food dishes, behind my bedroom bureau..recently, they've been making a nest on my bed behind the throw pillows!!!
Naughty birds....At any rate, I've tried most everything to get them to stop the nesting thing but not really successful. So, I put the grate back on the bottom of their cage and just try and keep them off guard as much as possible. ( lovebirds ARE tenacious little devils).
If you don't want them to breed, please take away the box. They'll lay irrespective but it won't be so easy and you aren't depriving them but not giving them the box...you are actually encouraging them which probably isn't a good thing. I had one session in January where they spent weeks laying on their eggs on the floor of the cage....under the newspaper. Since then, there has been a few eggs but they haven't shown any interest in laying on them.
by the way, please make sure that you have a cuttlebone ( extra calcium) in the cage for your girl at this time....if they do egg lay, it can deplete them of calcium and can cause problems.