Psychic has long been considered one of the most powerful types in Pokemon. In Generation 1, it was nearly unstoppable, barely having any weaknesses whatsoever. Over the years, this changed significantly, and they're not quite as overpowered now. However, they still have plenty to offer.
A significant portion of supporting moves are Psychic-type, and most Psychic Pokemon have a large movepool of non-Psychic moves, making them perfect for both coverage and support. One of the biggest factors determining what they have access to is their secondary type, and some are much better than others.
8 Dragon
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Much like Psychic, Dragon has long been considered a very powerful type. In fact, it was so powerful that the Fairy type was added in Generation 6 to balance it out somewhat. Combining the two will naturally make for a powerful combination, and indeed Psychic/Dragon Pokemon have access to some potent moves.
However, they come with some downsides. While they have a solid 6 resistances, they come with 6 weaknesses as well, meaning there isn't a great deal they can do without getting struck by something unfriendly. That said, the only Pokemon to currently hold the type are Latios and Latias, who have a great combination of speed and bulk.
7 Fighting
Combining types that are traditionally opposed often leads to exciting results. Fire/Water, for example, is a fantastic combination. However, the same can't be said for Psychic/Fighting. Pokemon that have it are often quite cool-looking, like Gallade, but functionally don't have a lot to offer.
The problem is that most Psychic attacks are Special, whilst Fighting attacks are Physical. This means most Pokemon can't invest in both stats effectively unless players are willing to use sub-par moves like Psycho Cut or Aura Sphere.
6 Fire
For players who want an offensively-focused Psychic Pokemon, Fire is a good place to look for secondary types. Fire is traditionally a very aggressive type, with little to no interest in non-attacking moves. Additionally, the Burn status condition halves the opponent's Attack, making it work defensively as well.
Fire comes out a bit more favorably than Dragons when it comes to type matchups. This type only has 5 weaknesses, which is still quite a lot, but it backs it up with 7 resistances. It's still likely to run into trouble from a well-built team, but it has just a bit more chance of getting away unscathed.
5 Flying
Flying is generally quite a balanced type. With such a variety of Flying Pokemon on offer, they can be both aggressive and defensive, with even a few supportive capabilities. They are traditionally a very fast type, too, which is always a plus, regardless of whether players want attack or support.
Unfortunately, it doesn't fare too well on type matchups. 5 weaknesses are difficult to contend with, especially with only 3 resistances to back it up. One of those is a 4 times resistance, which is nice, although no trainer will oppose a Psychic-type with a Fighting Pokemon anyway.
4 Dark
Much like Fighting, Psychic and Dark are two types that seem diametrically opposed to each other. In this case, however, this type combination makes for an interesting scenario. For one thing, Dark is another type with a rather large movepool, full of both aggressive and defensive moves.
The type matchups are pretty weird too. On the surface, 2 weaknesses and no resistances sounds like a raw deal, especially when one of those is a 4 times weakness. However, it enjoys immunity to Dark-type as well. It's a weird situation and one of the only combinations in the franchise to be immune to itself.
3 Fairy
Ever since the Fairy type was introduced in Generation 6, one of its most popular pairings has been with Psychic types. The visual style of the two types is often in alignment, and it makes it easy to retroactively assign the Fairy type to a lot of old Psychic Pokemon.
It fares pretty well on the battlefield, being neutral to the vast majority of attacks. It only has 3 weaknesses, which is a manageable number. It's backed up with 2 resistances, one of which is a 4x resistance. It means that most of the time, players will be dealing with neutral attacks, which makes things far more predictable.
2 Poison
Poison on its own isn't a great type. Perhaps it's just a fault in Game Freak's design philosophies, but Poison-type Pokemon are often pretty weak for various reasons. That said, when used as a secondary type, it can strengthen a Pokemon's capabilities.
Psychic enjoys a nice synergy with Poison. Once again, it has just 3 weaknesses, alongside 4 resistances, including a 4 times resistance. It makes Psychic/Poison Pokemon quite hard to take down, and with access to status conditions, it can be a real problematic type to face off against.
1 Steel
Far and away, one of the best type combinations in the entire franchise, it would not be an exaggeration to describe Psychic/Steel-type Pokemon as near-impenetrable walls. Psychic can be used very effectively as a defensive type, which pairs well with the best defensive type in the game.
With just 2 weaknesses and a whopping 9 resistances, opponents will have very few opportunities to get rid of it easily. It's ensured that a Pokemon like Bronzong has enjoyed extreme longevity in the competitive battling scene. They perhaps can't hit as hard as other combinations, but that doesn't matter when they can remain on the battlefield for ages.