To quickly summarize a long story.
Our dragonborn paladin started the campaign venerating Tyr, and was largely content with the relationship. Then, due to player request (multiclass to warlock) earned a pact with Nathair of the Summer Court. Seems to quite enjoy the play by play with the little dragongod. 
Problem, over the course of the campaign, the paladin has more or less begun to regard Tyr as distant and unhelpful, due largely to previous DM being vague, Nathair however, was commonly willing to talk. Naturally, this meant more interaction. 

Now, as current DM of the campaign, I would rule that Tyr, being Lawful Good, and having strict disciplines and tenets, is unsuited for the Paladin as a patron god. However, at the same time, Nathair is more or less portrayed as uncaring of the current state of the campaign and the party goals, seeking more to get the party and paladin to party in the Feywild, thus shirking their duties and leaving their worries behind.
As DM, I recognized the player-character is too chaotic-good to follow the typical/stereotypical paladin LG archetype, while being too disciplined to fully give himself over to Nathair's classic CG nature. So, I considered a third option. Odin, instead of Tyr. He seems to be more geared towards NG players, what with his 3rd edition portfolio.

My current idea is to offer Odin showing up in secret to a temple of Tyr, questioning the paladin about things, with the ultimate goal of determining if the character is suitable to fight under the banner of Odin. If the paladin accepts the change of god, I will continue to rule him as his current setup, with two divinely requested objectives to prove his worth and strengthen the influence of Odin in the Forgotten Realms.

The first goal: Plant a banner or spear of Odin throughout the world, so that Odin's ravens (Thought and Memory) can perch freely and observe things.
The second goal: Spread the worship of Odin. Not by preaching to crowds, but by finding heroic figures or civilians to aiding them. After all, Odin wants heroes at his side in Ragnarok, and the gods are strengthened by worshippers.

TLDR
I want opinions on this idea, and ideas or potential quests/rituals the character can enact to further their relationship with this god. Things like, offerings of mead and boar at temples, slaying of powerful monsters, paying tribute at temples, training a militia or otherwise defending people from giants or dragons, and so on and so forth.

Not being super versed in the pantheons of Faerun I was first "wha---" but I checked the Forgotten Realms wiki.  Clearly your tribute to Odin has to go to the Tears of Selune and rescue Odin's followers on the Rock of Bral.   Go Marvel Weird and have the threat be some sort of alliance between Loki, Mind Flayers, and a bunch of Lower Planes folks with sore feelings over something Odin did on one of his Lower Plane outtings.  Extra role playing challenge: whatever it was Odin did on the lower planes, the PC Palladin can actually appreciate the perspective of the fiends on account of being on the receiving end of whatever Odin got up to.