Ezreal's long range makes him a good candidate to play a weak side lane which means his support or jungler can roam other lanes and leave him from time to time in the bottom lane. His Q is an excellent poking ability that he can spam as it has a low cooldown. He can also use it to quickly kill minions even in the early game. His long range as well as his ultimate clears minion waves fast making roaming support champions the best pair for Ezreal.
Nami takes the first place in this list as she is also a good poke champion and can easily roam to other lanes thanks to her ultimate. Nami can boost Ezreal's laning phase during the early game thanks to her E. She can enhance Ezreal's Q and add a slow effect to it as well as an increase in the damage output. If they manage to take over the lane during the early game and shut off the enemy ADC then, Nami can roam to other lanes.
Nami has a powerful gank as he can cast her ultimate from the fog of war coming from the side, surprising the enemy in whatever lane she decides to gank. She can also help her allied champions play defensively as she can heal with her W.
Aside from Nami's roaming potential, she also has strong burst damage having abilities that scale with ability power. Almost all of her abilities can damage enemies meaning she can return to the bot lane with Ezreal and take lane priority. She can also help Ezreal secure kills as all of her abilities give a bit of movement speed boost to Ezreal.
Being the champion with the strongest engage makes Leona a relevant support for Ezreal. She is a tanky champion that can engage for Ezreal at any point in the game. She can surprise gank other lanes with her ultimate especially if she has a hex flash.
With Ezreal being great at playing the weakside lane, Leona can take this advantage to build boots of mobility and even be a roaming support all the way to the top lane. If they manage to take over the bottom lane by being aggressive, Leona can leave Ezreal as long as he has a huge lead against the enemy. But if Leona decides to stay, her aggressive playstyle combined with Ezreal's quick follow-up can be a huge nuisance for the enemy team.
Soraka probably is the best ezreal support out there as she is a potent enchanter that can be useful when playing defensively. Her heals and item builds during the late game is overpowered as she can simply keep on healing Ezreal as he kites their enemies. Soraka can also trade pokes during the early game and the heal that comes along with her Q acts as a self peel to mitigate the damage she receives.
Soraka can also be very useful during team fights thanks to her heals. She can spam her W and even user her ultimate if enemies have AOE damage. Her silence greatly slows enemy carries down especially the ones with strong combo abilities. However, you need to have high knowledge about kiting and positioning as Soraka is a squishy champion that can be taken out easily.
Lux and Ezreal in the bot lane is a dangerous duo as they have far reach with their abilities and low cooldowns on offensive spells. They can both spam their abilities and easily take control of the lane. Both of their ultimates have strong burst damage making it easy for them to take control of the lane. Once Lux lands her combo, enemies will have a hard time to try and survive as Ezreal can quickly follow it up with his own combo as well.
Ez's laning phase with Lux is quite strong and if they manage to win the lane, Lux can build carry and mage items to prepare for the late game. Lux has excellent wave clearing thanks to her ultimate making her a useful buttet when enemies try to split push during a major objective fight.
Alistar is a solid champion when it comes to peeling for his ADC or even engaging. His tanky nature allows Ezreal to keep on hitting enemies from afar without receiving retaliation. His W can be used to easily engage enemies and take over the lane at the start of the game and, he can also use it for a quick disengage especially if champions like Master Yi charge toward Ezreal.
Alistar does a great job at protecting Ezreal making him a great pick to play with especially because Ezreal needs a few items before he reaches his power spike. His ultimate also allows this duo to tower dive enemies and stick with the enemy ADC and keep on inflicting crowd control abilities on them.
In summary, all champions that can roam and help Ezreal achieve an early game lead are the best picks to play with. Ezreal's pokes are really great especially if he has a support that can improve its damage. Playing with an Ezreal ADC doesn't really require high knowledge as he is pretty straight forward, dstay back and throw his abilities at enemies. Pick these champions and climb your ranks as a support.