Much like with clerics and the different paths that they can select, the idea is to provide blackguards with a similar path system. As blackguards are warriors blessed by dark entities, the two proposed alternatives are ones sworn to demonic and undead service.
The idea behind these thematic choices is to both stay true to the class concept and provide different roleplaying and mechanical opportunities for players.
The lichguard
Much the same as the base blackguard but swapping the sneak attack progression with a gradual damage immunity or granting some of it as elemental resistance (potentially wrapping it into their capstone ability)
Lose access to summon fiend but access to higher tier undead summons
Lose access to divine synergy but get an improved divine shield that gives CHA mod regeneration for the same number of rounds
Aura of despair and unholy accuracy are replaced with a feat that gives 50% chance to turn a critical hit to a normal one
Due to how much of a tightrope balancing is and noticing that how limited DI is I can’t really give any numbers I would be comfortable with aside from a tentative 10-15% DI at level 20
The Fellguard
Much like the lichguard this variant changes sneak attack progression for an increasing list of arcane spell like abilities on a cooldown, with more higher-level spells being slowly added as they reach higher levels
Spells proposed include, fireball, vampiric touch, haemorrhage, darkbolt, chain lighting, hell inferno, vermilion stars, firestorm, powerword: bleed
Lose access to summon undead
Lose access to divine synergy but gets an improved divine might that has a chance to refresh any fellguard spell like abilities while it is active
Aura of despair and unholy accuracy are replaced with access to a select few 9th circle spells
The idea for this is to be an aggressive spell slinger knight, limiting the spells gained to purely offensive ones means that they are encouraged to be more aggressive than a traditional blackguard
There are other suggestions that could be done like giving lichguard access to heroic shield to protect their summons or giving fellguard imp familiars or changing bulls' strength but the core idea is that blackguards are overall all-rounders, the variants are meant to excel in one area while sacrificing another
I think it's important that they both lose access to divine synergy and their +6 corrupt weapon (making it cap out at +5) in order to both different between the different variants and allow them to have interesting class abilities without contributing as heavily to powercreep.