i would be sure of a FEW things. they can be super cute and sweet and intelligent birds....
but ask yourself the following first:
are you willing to tolerate a crazy psychotic monster for a few weeks to months out of the year if your bird winds up being a hen? they get hormonal and nesty usually and they can be VERY aggressive and bite very hard and with little warning. it can make feeding them very hard. even if a female is super sweet when young, once the hormones kick in, they can be very aggressive. some times of the year they are really bad, then other times they are just fine and maybe a bit nippy.
are you willing to get your hand nipped off if yours ends up being very cage aggressive (males tend to just nip, females tend to latch on and not let go, they got a death grip)
lovebirds are very cage territorial and generally do not like other birds or people in their cages and will ferociously defend their space. some birds are worse than others, some arent that bad at all. its a common problem with lovebirds, even when sweet as babies.
are you willing to house the bird in a whole other room if this bird decides it has a deathwish for your cockatiels? lovebirds generally do not do well mixed with other birds and can often try to kill other birds, and especially bite toes if they land on the lovebirds cage, or lovebirds think it is a game to go onto other birds cages and try to grab toes and feathers through the bars. you may have to have a whole separate room for this bird. they CAN kill cockatiels.
are you aware of the loud noises they make? this video here of my cockatiel in another room, you can hear the lovebirds in the room over at their most annoying time lol
Dally Playing With Toby's Toy - YouTube
that in your ear with one on your shoulder will make your ear ring, and they chatter all day. while not LOUD, they are slightly louder than cockatiels, and they hardly ever shut up.
i love lovebirds, but they do come with some serious drawbacks. theyre so active and funny and playful you will never cease to be entertained. they can be so interactive and theyre like a big parrot. they need a fairly large cage because of how active they are.
they are heavy chewers and LOVE paper--so protect important documents and photographs and anything hanging on your walls lol
if you can handle all the possible drawbacks, then its a great choice. just remember, hormones will hit around 6-8 months, and thats when you might see some attitude changes.
not all are monster birds, but most hens are. its just how they are, theyre not mean birds, theyre just aggressive and territorial and maybe a bit crazy
but the upsides have a LOT of good things, its just hard to weigh which end of the spectrum with them.
males can be nippy too but generally are more laid back and gentler than hens. but hens can make excellent pets too, they just require some caution if you get some crazy one like we got with munch!
they are prone to plucking. munch is a self mutilator because of her obsessive compulsive disorder. they are very intelligent and need to have a lot of toys and enjoy moderately difficult foraging toys. they have a MUCH stronger beak than a tiel and can destroy a lot of things. so be sure to have a lot of toys they can chew. they like making noise and chasing things. so bells and balls are fun toys for them.
as for basic bird questions...
space wise, are you able to house another bird, in another room (possibly full time if the lovebird is aggressive enough)?
do you have a lot of time to give to the cockatiels and a lovebird? single lovebirds need a LOT of one on one time. a lot more than a cockatiel. they do need to be handled every day or they can revert.
do you have the finances to care for another bird?
just some thoughts.
if you can, go for it! lovebirds are great birds, but be VERY careful with them. you will be amazed by how cute and intelligent and playful they are.
for the record, my hen is handraised. handfed from the day she was born. shes bold and aggressive and shows no fear of people, yet she has made one of the best improvements and has to be handled differently than the other birds. shes much more intelligent than all of them and we swear shes gonna take over the world... but every day she loves to interact with us, even if she doesnt always want to be hands on.