Paras is quite a popular Pokemon in Little Cup, and for a good reason. Spore is one of the best moves in the game, being a 100% accurate sleep-inducing move. Taking a Pokemon out of combat is an excellent tool to have, especially in a metagame where every turn counts. This set uses all of Paras' strengths: its decent defenses, its above average Attack, and of course, Spore. This set comes with a couple of options, first being the second attacking move. Seed Bomb is a nice STAB move; however, while Aerial Ace is not very powerful, it hits other Paras and more importantly Croagunk. Bug Bite is a great move to use in Little Cup, with Oran Berry being the most common item in the metagame, even though X-Scissor will hit a little harder. With Paras' decent Attack stat, it can put the hurt on Pokemon switching in. Synthesis is recommended in the last move slot because of the many Pokemon who use Protect; Paras will likely get at least a couple chances to heal himself.
Alternatively, Paras can use the double status approach by using Stun Spore in the last slot. The strategy is fairly simple, starting off with Spore. After the opponent is asleep, you can either predict their incoming switch and Stun Spore, or hit the sleeping Pokemon with a powerful STAB attack. Paras laughs at most priority attacks, so you don't need to worry about those outpacing you. This is the main reason Paras really benefits from using paralysis to outpace its opponent. This set does not need cover Croagunk, because Paras can generally take him out with paralysis and strong STAB attacks.
With its monstrous Fire-type weakness, Paras will lure out Fire-type attackers, and as such, needs something to sponge those hits. Pokemon like Ponyta and Houndour work very well with Paras, as Paras' weakness reliably gets them Flash Fire boosts. Paras also has a huge weakness to Flying-type attacks, which will mainly come from Pokemon like Taillow, Gligar, and Doduo. These Pokemon are much easier to wall, because their STABs are all resisted by the same types. An example is Bronzor, who resists Normal-, Flying-, and Ground-type attacks. Paras has a terribly annoying Rock weakness, meaning it can only switch in a certain amount of times before it gets knocked out by Stealth Rock. Paras works best with Rapid Spin support from Pokemon such as Squirtle or Anorith, especially since, if your opponent uses Gastly (a common switch-in to Paras due to it resisting both STABs), their Ghost-type will likely get put to sleep or weakened by Paras. This gives Squirtle and Anorith a much better chance to rid the battlefield of Stealth Rock.
If you opt for Stun Spore, many slow and powerful Pokemon benefit from paralysis support. Cubone is a great example; with its monstrous Attack and great coverage it will surely land a few KOs as long as it outspeeds the opponents. Substitute sweepers can also take advantage of paralysis, using Substitute until the foe is unable to attack, followed by either KOing that Pokemon or setting up. Paras also has a very unique ability that should be taken advantage of, especially with Stealth Rock being so common. Using Pokemon like Rhyhorn or Onix with Paras is an extremely good tactic for luring Water-type attacks that heal Paras up during the battle, allowing it to keep on taking the hits it needs to be taking for your team.