I've also recently purchased some lovebirds & had the same problem at first.
I was told by the pet shop guy that most people dont handle or take out their lovebirds, but you can if you want but it will take a while.
So, everyday I just stick my hand into their cage and move it as near to them as possible without scaring or stressing them. Because I have had them for 1 and a half months now I can nearly touch them. I suppose it's just a matter of trust... Talk to them and whistle to them as well.
Oh yeah, I only started puting my hand in the cage after a week or so when they had settled down.

Oh and just a bit of advice. (as I had this problem) I called the pet place where I bought my lovebirds from because my birdies where fighting, he said it is perfectly normal for this to happen in the first ish week, they just fight to see who is in charge/the dominant one!

But if they start drawing blood then you may have to seperate them.

but this shouldnt happen!

Just remember that I am not a bird expert so if your really stuck and feel you would like a more definite answer just ask a vet or somone who is expierienced.
Good luck!
