The answer, rules as written, is no.

In your pit fiend quote, as we can see, we need a good aligned silver weapon to overcome both is regeneration and damage reduction.

Regeneration:

 

A pit fiend takes normal damage from good-aligned silvered weapons, and from spells or effects with the good descriptor.

If an angel with a silver long sword attacks the pit fiend the angel will automatically overcome the damage reduction of the fiend since the sword is made of silver and the angel's attacks will be treated as good aligned and damage reduction is pretty specific on this point:

[...] A creature with an alignment subtype (chaotic, evil, good, or lawful) can overcome this type of damage reduction with its natural weapons and weapons it wields as if the weapons or natural weapons had an alignment (or alignments) that match the subtype(s) of the creature. Ammunition fired from a projectile weapon with an alignment gains the alignment of that projectile weapon (in addition to any alignment it may already have).

Regeneration does not have a similar entry so the angel's weapons are not aligned in that regard.

Tl;dr: No, alignment subtype does not allow to bypass regeneration (only damage reduction) as a general rule.

The answer, rules as written, is no.

In your pit fiend quote, as we can see, we need a good aligned silver weapon to overcome both is regeneration and damage reduction.

Regeneration:

A pit fiend takes normal damage from good-aligned silvered weapons, and from spells or effects with the good descriptor.

If an angel with a silver long sword attacks the pit fiend the angel will automatically overcome the damage reduction of the fiend since the sword is made of silver and the angel's attacks will be treated as good aligned and damage reduction is pretty specific on this point:

[...] A creature with an alignment subtype (chaotic, evil, good, or lawful) can overcome this type of damage reduction with its natural weapons and weapons it wields as if the weapons or natural weapons had an alignment (or alignments) that match the subtype(s) of the creature. Ammunition fired from a projectile weapon with an alignment gains the alignment of that projectile weapon (in addition to any alignment it may already have).

Regeneration does not have a similar entry so the angel's weapons are not aligned in that regard.

Tl;dr: No, alignment subtype does not allow to bypass regeneration (only damage reduction) as a general rule.

The answer, rules as written, is no.

In your pit fiend quote, as we can see, we need a good aligned silver weapon to overcome both is regeneration and damage reduction.

A pit fiend takes normal damage from good-aligned silvered weapons, and from spells or effects with the good descriptor.

If an angel with a silver long sword attacks the pit fiend the angel will automatically overcome the damage reduction of the fiend since the sword is made of silver and the angel's attacks will be treated as good aligned and damage reduction is pretty specific on this point:

[...] A creature with an alignment subtype (chaotic, evil, good, or lawful) can overcome this type of damage reduction with its natural weapons and weapons it wields as if the weapons or natural weapons had an alignment (or alignments) that match the subtype(s) of the creature. Ammunition fired from a projectile weapon with an alignment gains the alignment of that projectile weapon (in addition to any alignment it may already have).

Regeneration does not have a similar entry so the angel's weapons are not aligned in this case.

Tl;dr: No, alignment subtype does not allow to bypass regeneration (only damage reduction) as a general rule.

The answer, rules as written, is no.

In your pit fiend quote, as we can see, we need a good aligned silver weapon to overcome both is regeneration and damage reduction.

Regeneration:

A pit fiend takes normal damage from good-aligned silvered weapons, and from spells or effects with the good descriptor.

If an angel with a silver long sword attacks the pit fiend the angel will automatically overcome the damage reduction of the fiend since the sword is made of silver and the angel's attacks will be treated as good aligned and damage reduction is pretty specific on this point:

[...] A creature with an alignment subtype (chaotic, evil, good, or lawful) can overcome this type of damage reduction with its natural weapons and weapons it wields as if the weapons or natural weapons had an alignment (or alignments) that match the subtype(s) of the creature. Ammunition fired from a projectile weapon with an alignment gains the alignment of that projectile weapon (in addition to any alignment it may already have).

Regeneration does not have a similar entry so the angel's weapons are not aligned in that regard.

Tl;dr: No, alignment subtype does not allow to bypass regeneration (only damage reduction) as a general rule.