why I think Shulk, Jigglypuff, Greninja and Rob is great secondaries are:
Shulk:
+ he has good range, can jump high, run fast, can deal fast damage and can kill fast thanks by his monado arts!
+ many things are possible with him and he has lot of trickery and many ways to go, just like Jr.
+ his SH Nair is great approching tool and way to get through projectiles.
- he can be gimped easy, even with monado jump!
Jigglypuff:
+ she is a pure WoP thanks by her amazing recovery, lightness and attacks
+ Many of her attacks are priority, making her against example shulk a piece of cake thanks her attack has higher priority than monado
+ rest kills at 40 on light character and 50 on medium+heavy
+ some Disjoint hitboxes like Jr
- lacks projectiles, but doesnt really need it
- lightness is a double-edged sword, it makes her die easier
- shield break makes her instant KO
Greninja:
+ Greninjas speed is a big plus
+ Greninjas jump and recovery are top-notch
+ has projectile and a "push off" water stream
* tricky to master
- lacking kill moves
Rob:
+ similiarities in attribution between Jr and Rob makes rob a easy player to play as yet plays at completely diffirent playstyle
+ has 2 great projectiles that easy chip of damage and for approches
+ great kill options in many ways
+ reflecting move
- even if they are similiar in attributes, they can share the same weakness
these 4 removes some of Jr greatest weaknesses, but they do not remove all of his and they self either have their own weaknesses (that Jr removes) or that they have for their own!
I think the things secondaries for jr need to cover for are (at least for the way i play him)
1. His kills will often rely on good reads, leading to potentially high percents/late kills against unpredictable opponents.
2. His moves are very telegraphed and punishable. Hes a very momentum based character and when momentum isnt yours he becomes easily punished for almost everything.
3. He can often be too slow to reliably punish some of the faster characters in the game.
To adress other complaints I often read about him:
Gimpable; with all the options and time you have using 2 jumps and cart+jump or spinout, AND airdodging or attacking with great priority out of upB, i dont think gimping is one of the bigger problems. Yes, it does happen and you feel helpless, but i dont think it should be happening often enough and consistently enough for it to be a reason to change character. Even so, most secondaries wont suffer the same gimping problems as jr anyway, so i dont think its worth considering.
Grab; his grab kinda sucks... But it also doesnt really set up into much. Its not worth using often anyways. Yeah its not great, but every character has a few bum moves. Jr has plenty of other option anyways.
He's slow/sucks at approaching/relies on the cart; he's definitely not the slowest and he does have cart to compensate. And his approaches once in the cart can be extremely varied and easy to space as long as you dont commit to unsafe options or to using the same patterns over and over. A lot about this has been said already, so ill leave it at that.
All that being said, choice of secondary clearly depends on how you play jr and the other characters. Personally, I feel as though good secondaries for him are characters with fast, safe options and reliable kill moves.
My BJr tends to put himself all out there. He racks up damage very quickly but can also easily get thrown off his game and become quickly overwhelmed. I think a good secondary should be able to punish this with a steadier game.
My suggestions would be:
Jigglypuff
(Pros have already been said. Good priority, strong attacks. Very attack reliant instead of special reliant. She feels like the opposite of bjr, but her air game feels like it controls almost the same)
Luigi
(Has some combo game but feels safer than bjr. Also has some reliable kill options)
Ness
(When chasing offstage just isnt working out for some reason, sit back and pk thunder! He's also pretty good at not getting overwhelmed. Back throw is a very good kill option and his grab is superb if youre feeling like youre having trouble killing)
Rosalina
(Shes really good and really safe. Maybe she isnt the best theoretical secondary to bjr but personally she has worked wonders at times when I was getting whooped. I dont put much weight into tiers but i think her tier status also adds an intimidation factor that Bjr often wont have)
Yoshi
(Not my personal choice, I suck with him but people have seemed to compare him to luigi so maybe someone else can expand on this. Also most of jr's top tier worst MUs seem to report trouble with yoshi. Iunno just thought I'd include it.)
These are just my thoughts, feel free to discuss or disagree
this is just based on personal experience and what i notice watching more expert bjr players