Ghost / Dragon This is one of the ones I really like. Dragon has a lot of resistances and host gives it a couple more imunities making this a great defensive typing. It resists Volt-Turn and has been said, dragon STAB really benefits from trapping. The fact that both its STABs have immunities also mean that trapping becomes more important to prevent a switch into an immunity. Anchor Shot does SE damage to one of its weaknesses and it gets STAB on Spirit Shackle. And STAB Spirit Shackle can also help chase away the other Ghosts that are immune to our traps. Immunity to one of Tomohawk's STABs is also a bonus. The immunity to counter trapping is also nice. A dark weakness is a pity, but Pursuit and Knock-Off are going to be less of an issue when not switching out and when using a Z-crystal. In addition, I believe that Fairy-coverage is a good idea anyway to give a small niche to Fairium Z Fairy Lock users.
Offensively, dragon hits most things neutrally, and Ghost hits the Steels and Fairies that wall it neutrally.
Ground/Steel This is another one I really like. Steel is another great defensive typing that gives an important immunity to both a type, and an important status. It also provides STAB on Anchor Shot. Ground shuts down Volt Switch completely, meaning that a Ground typing traps more mon than any other. We also resist U-Turn. Ground is also an amazing offensive typing, especially in the CAP metagame. That said, there are those who are immune to it, making trapping to avoid switching into an immunity more appealing. We're also immune to sandstorm damage which can be helpful and get STAB Sand Tomb. We also quadruply resist Stealth Rock which makes coming in at the right time to trap much easier.
Offensively, Ground is an amazing typing, especially in the Cap metagame, and while Steel isn't an amazing offensive type, it hits the Flying and Grass types that wall Ground neutrally.
Dragon/Flying While this typing has benefits, I think that a 4x weakness, especially to such common coverage as ice, is very bad for a mon that has to take multiple hits to do its job properly.
While these are good offensive types, they are both walled by Steel, necessitating Fire/Fighting coverage which limits us.
Dragon/Fighting While not as bad as ice, especially with Anchor Shot availability, a 4X weakness to Fairy still does us no favours.
Offensively, these are great types, but both walled by Fairies, meaning that Anchor Shot is pretty much the only trap move that will be run.
Steel/Dragon This is another typing I really like. Steel and Dragon are both great defensive typings and an immunity to being poisoned is really helpful. As well as to the Poison type and sandstorm. We also get STAB Anchor Shot. The benefits of trapping to dragon STAB have already been discussed. A resistance to Stealth Rock is also great. As is a resistance to Volt-Turn.
Dragon is great offensively and Steel donks the Fairies that are immune to it. Admittedly, other Steels do give it issues, but I think that the other points make up for this.
Steel/Grass While a great defensive typing, a 4x weakness to a common offensive typing like fire does hurt.
Offensively, neither of these is an amazing type. They're both walled by Fire as well, for example.
Ghost/Ground This is my favourite typing for this concept. Immunity to Volt-Switch, 3 typings, and counter-trapping. A great offensive STAB in Ground. Both STABs have immunities to encourage trapping. STAB on both Spirit Shackle and Sand Tomb. STAB Spirit Shackle chases away other, untrappable Ghosts. Resistance to U-Turn. Immunity to one of Tomohawk's STABs. And, as said earlier, dark weakness is not too much of an issue.
As I said earlier, Ground is amazing offensively and Ghost hits Flying neutrally and as I said, we want to hit ghosts super-effectively if possible. Admittedly, Normal/Flying types wall us, but most of them aren't that relevant and can be dealt with with coverage.
Flying/Ground I've mentioned why I think a 4X ice weakness is a bad idea.
Offensively they're pretty great admittedly, doing SE damage to a lot of things.
Fairy/Ground This isn't bad. It does have all the advantages of ground I highlighted earlier and U-Turn resistance. Fairy also makes the Fairium Z set I mentioned more appealing. It also messes up Tomohawk, which is nice. And a resistance to dark is pretty nice. It also provides another immunity. I still prefer the advantages other typings give though.
Offensively, as said, Ground is great and Fairy's pretty strong too, with Ground covering its weak points.
Dark/Ghost While the reduction of U-Turn to a neutrality is there, this does offer the other benefits of the Ghost typing while also being immune to Tomohawk's prankster, which is nice. It also is not weak to Dark.
Offensively, they're a bit redundant admittedly.
Psychic / Fighting I'm a bit worried about a weakness to flying with Tomohawk and Lando out there.
Offensively, they are walled by other psychic types, though Fighting is a pretty good offensive typing that has some of its weaknesses, such as to Poison patched by Psychic.
ghost/fairy I've mentioned the advantages of both Ghost and Fairy already. Dark becomes a neutrality here. Not a bad choice.
Offensively, Fairy and Ghost are pretty good as well.
Ghost/Normal Three immunities is just lovely, especially when one is to the Ghosts that otherwise mess us up and we can hit them back Super-Effectively. Again, both STABs have immunities. I have been convinced that this is a pretty good choice.
Normal's offensive problems are also patched up by Ghost, with Ghost doing SE damage to the Ghosts that are immune to Normal and which we want to chase away.
Flying / Steel I really don't want a weakness to Volt-Switch if possible.
It's also walled by other Steels offensively.
Ground / Fighting Quadruply resistant to Stealth Rock, immune to Volt-Switch, resists U-Turn. Great offensive typing where both STABS have immunities. One of those immunities being Ghost is unfortunate though, and as I said earlier, as is weakness to flying.
Admittedly, it does struggle offensively against Flying, but they are pretty good offensive types otherwise.
Pure Electric I'm reasonably neutral on this one. It resists Volt-Switch and has a good STAB that has immunties and has a good defensive typing. Ground coverage is common though and it doesn't have a lot else going for it.
Electric is pretty nice offensively, but leaves us walled by Ground and Grass and makes carrying Ice coverage very predictable.
Electric/Ghost Well I've already discussed the benefits of both Electric and Ghost. They don't go badly together.
Ghost does patch up Electric's offensive shortcomings.
Dragon/Fairy A dragon that turns a weakness to an immunity and another to a neutrality is pretty good. I've already discussed the benefits of both typings and they go well together.
Offensively, however, Fairy doesn't really strengthen Dragon's shortcomings much, still being walled by Steel and other Fairies.
Fairy/Steel Fairy and steel have both been discussed and one of Fairy's weaknesses becomes an immunity here. It's a pretty good combo.
Offensively, however, it leaves us walled by Fire types.