Here is some information regarding what some very good abyssites are to have for Abyssea. this same info can be found on Wiki

Ivory Abyssite of Sojourn

Speaking with Cruor Prospectors in Abyssea and purchased with 6000 Cruor in Abyssea - La Theine, Abyssea - Konschtat or Abyssea - Tahrongi
Notes:
Extends duration of Visitant Status by 3 minutes per Traverser Stone. Effect stacks with other Abyssites of Sojourn; Jade, Indigo, Emerald, Sapphire and Scarlet (+3,+6,+9,+12,+15,+18), making each Traverser Stone give between 33-48 minutes, depending on the number of Abyssites of Sojourn acquired.

Scarlet Abyssite of Sojourn

Extends Traverser Stone duration by +3 minutes, obtained by defeating Ovni in Abyssea - La Theine Plateau

Jade Abyssite of Sojourn

Extends Traverser Stone duration by +3 minutes, obtained by defeating Mielikki in Abyssea - Attohwa

Sapphire Abyssite of Sojourn

Extends Traverser Stone duration by +3 minutes, obtained by completing the quest "Destiny Odyssey" in Abyssea - Misareaux, must have level 4 fame in Aby-Misareaux and completed a pre-requisite quest.

Indigo Abyssite of Sojourn

Extends Traverser Stone duration by +3 minutes, obtained by defeating Assailer Chariot in Abyssea-Grauberg

Emerald Abyssite of Sojourn

Exteneds Traverser Stone durationg by +3 minutes, obtained by defeating Waugyl in Abyssea-Altepa

Azure Abyssite of Celerity

Obtained by: Killing Tonberry Bedevilers or Cryptonberry Occultist in the Abyssea - Konschtat zone.
Notes:
Traverser Stones replenish 4 hours sooner. Abyssite also effects all current stones, re-calculating the number of stones that Joachim is currently holding for you. Effect stacks with that of Crimson Abyssite of Celerity and Ivory Abyssite of Celerity. Holding all 3 will allow you to receive a new Traverser Stone every 8 hours.


Crimson Abyssite of Celerity

Obtained by: Completing the quest Whither the Whisker in Abyssea - Vunkerl
Notes:
Traverser Stones replenish 4 hours sooner. Abyssite also effects all current stones, re-calculating the number of stones that Joachim is currently holding for you. Effect stacks with that of Azure Abyssite of Celerity and Ivory Abyssite of Celerity. Holding all 3 will allow you to receive a new Traverser Stone every 8 hours.

Ivory Abyssite of Celerity

Obtained By:
Purchased from Cruor Prospector for 9000 cruor in Abyssea - Grauberg, Abyssea - Uleguerand or Abyssea - Altepa
Notes:
Traverser Stones replenish 4 hours sooner. Abyssite also effects all current stones, re-calculating the number of stones that Joachim is currently holding for you. Effect stacks with that of Azure Abyssite of Celerity and Crimson Abyssite of Celerity. Holding all 3 will allow you to receive a new Traverser Stone every 8 hours.

Ivory Abyssite of Avarice

Obtained By:
Obtained by purchasing from the Cruor Prospector in Abyssea - Attohwa, Abyssea - Misareaux and Abyssea - Vunkerl for 8000 Cruor.
Notes:
Provides the player the ability to hold onto another Traverser Stone. Along with the Viridian Abyssite of Avarice and Vermillion Abyssite of Avarice, the player may hold up to 6 stones on them.

Viridian Abyssite of Avarice

Obtained by killing Ephemeral Clionid or Manananggal or Quetzalli in Abyssea - Tahrongi. Low chance to obtain by person who claimed enemy upon its death << Changed to all pt/ally members in May 2011 update.
Notes:
Provides the player the ability to hold onto another Traverser Stone. Along with the Ivory Abyssite of Avarice and Vermillion Abyssite of Avarice the player may hold up to 6 stones on them.

Vermillion Abyssite of Avarice

Obtained by completing the quest Imperial Espionage II.
Notes:
Provides the player the ability to hold onto another Traverser Stone. Along with the Ivory Abyssite of Avarice and Viridian Abyssite of Avarice, players may hold up to 6 stones on them.

Sapphire Abyssite of Furtherance

Defeating Flame Skimmer - Abyssea-Misareaux
Notes:
Attribute bonuses and other beneficial effects will gain greater potency. Normal attribute bonuses from the Cruor Prospector give +10 to stats, but with this key item, they will give an increase of Attribute bonuses and other beneficial effects will gain greater potency. It is possible to get another increase of +10 stat boost from the Scarlet Abyssite of Furtherance.

Ivory Abyssite of Furtherance

Obtained By:
Purchased from Cruor Prospector for 7500 cruor in Abyssea - Grauberg, Abyssea - Uleguerand or Abyssea - Altepa

Viridian Abyssite of Merit

Obtained By:
Defeat either Bhumi, Mictlantecuhtli or Manananggal in Abyssea - Tahrongi.
Notes:
Increases the effect of HP and MP bonus enhancement granted by Cruor Prospectors by 10% and 5% respectively. Enhancement bonuses may increase further with the addition of other Abyssites of Merit: Azure, Jade, Ivory, Indigo and Sapphire.

Jade Abyssite of Merit

Obtained By:
Possible drop from defeating Warbler in Abyssea - Attohwa
Notes:
Assumed to have similar effect as Viridian Abyssite of Merit which raises the Cruor Prospector HP and MP enhancements by 10% and 5% respectively. Enhancement bonuses may increase further with the addition of other Abyssites of Merit: Viridian, Azure, Ivory, Indigo and Sapphire.

Ivory Abyssite of Merit

Obtained By:
Purchased from Cruor Prospector for 6000 cruor in Abyssea - Grauberg, Abyssea - Uleguerand or Abyssea - Altepa
Notes:
Increases the effect of HP and MP bonus enhancment granted by Cruor Prospectors by 10% and 5% respectively. Enhancement bonuses may increase further with the addition of other Abyssites of Merit: Azure, Sapphire, Jade, Indigo and Viridian.


Indigo Abyssite of Merit

Obtained By:
Defeat Xibalba
Notes:
Increases the effect of HP and MP bonus enhancement granted by Cruor Prospectors by 10% and 5% respectively. Enhancement bonuses may increase further with the addition of other Abyssites of Merit: Viridian, Jade, Ivory, Sapphire and Azure.

Sapphire Abyssite of Merit

Obtained By:
Completing the quest Wanted: Medical Supplies in Abyssea - Misareaux
Notes:
Assumed to have similar effect as Viridian Abyssite of Merit which raises the Cruor Prospector HP and MP enhancments by 10% and 5% respectively. Enhancement bonuses may increase further with the addition of other Abyssites of Merit: Viridian, Jade, Ivory, Indigo and Azure.


If you need any help with getting these abyssites, please let me know ingame or reply on the forum!