The Beloved of Valarian, as you have noticed, isn’t really intended for Paladins. You can get in (and wind up with both a unicorn and another mount, which could itself be a unicorn), but you don’t progress any of those abilities, which means stagnating your Smite, your spells, and that mount that you’re interested in.

Really, the class is for Rangers to become quasi-paladins, because you can just

Be a Paladin, have a Unicorn, worship Valarian, call yourself Beloved

The primary class feature of the Beloved of Valarian class is the unicorn companion. Well, a Paladin can just have one of those.

In the Dungeon Master’s Guide, page 204:

A paladin of 6th level or higher can use a [...] unicorn [...] as a mount.

So instead of getting a not-unicorn special mount at 5th level, get a unicorn at 6th level. You count as one level lower than your actual paladin level for the purposes of your special mount’s features.

Then worship Valarian, and you’ll effectively be one of the Beloved. A reasonable DM should have no problems with you calling yourself one/being treated like one in-character, either.

This is actually better than what a Beloved of Valarian gets, because your Special Mount improves with level, while the Beloved’s does not aside from the Telepathic Bond and Celestial Charger class features. Paladins instead receive an Empathic Link, though, and the Celestial template doesn’t do much to an already-intelligent unicorn. Despite not having the Celestial template, the unicorn is “from the celestial realms.”

Otherwise, you’re lacking a couple of +2’s to wilderness-y skills; you can easily get these from feats if you desire them. Timelessness, Uncanny Dodge, Nature’s Understanding, and Wood Repulsion aren’t very high-impact features, though the Timelessness is a nice one from a flavor perspective. One solution would be to be a race that gets Timelessness anyway; another could be to just ask the DM for it since it’s not really going to change the game, just change your character’s outlook on life.

The hard ones are ethereal jaunt and mass baleful polymorph. They’re both just once per day, but they’re also both reasonably powerful and fairly flavorful. These you would simply have to accept you aren’t going to get without actually taking the Beloved of Valarian class.

Unless your DM agrees to work with you:

Were I your DM, I’d work with you to build a feat chain for high-level Paladins of Valarian to get these features. Maybe something like these:

Beloved

Requirement: Must be a paladin of Valarian with a unicorn as a Special Mount

Benefit: You gain the Timelessness quality, add Knowledge (nature) and Survival and paladin class skills, and add the following spells to your paladin spell list:

1st: calm animals, charm animal, delay poison, detect snares and pits, entangle, eyes of the avoral, longstrider, pass without trace, speak with animals

Special: If you turn away from the faith of Valarian, you lose this feat and any feats that require it. You regain this feat if you return to the faith (including any atonement that may be necessary).

Because you can’t get the unicorn mount until 6th level, you can’t take this feat any earlier than that, either.

Entrusted

Requirement: Beloved

Benefit: You may, once per day, become ethereal as if by the ethereal jaunt spell cast by a sorcerer of your paladin level.

You also add the following spells to your paladin spell list:

2nd: barkskin, hold animal

3rd: heart’s ease, neutralize poison, remove disease, water walk

Since it requires Beloved, you don’t get this until level 9, the same level as a Beloved of Valarian. Also, you don’t need special rules about sharing the spell with your mount, because you have the Share Spells feature.

Spear of Valarian

Requirements: Entrusted, ability to cast 4th-level Paladin Spells

Benefit: Once per day, you may cast a special version of the baleful polymorph spell that affects all evil creatures within 30 feet of you (as a 10th-level druid). Affected creatures are transformed into harmless Diminutive mammals (rabbits, squirrels, or the like) or Fine vermin (nonthreatening spiders, centipedes, or the like). All affected creatures are transformed into the same type of creature. See the baleful polymorph spell description in the Player’s Handbook for details.

You also add the following spells to your paladin spell list:

4th: blinding beauty, commune with nature, freedom of movement, spear of Valarian

The requirement of 4th-level Paladin Spells puts this to 15th level; a bit earlier than when a Beloved of Valarian gets it, but reasonable enough.

These allow you to be a paladin, while earning some of the special features that Beloveds get in a timely fashion, without making them “freebies.”

Confirm the Fluff with the DM

The only thing important about the exalted feat Nymph's Kiss (BE 44) is what it is (an exalted feat) and what it does (the feat's Benefit). Everything else about that feat is purely descriptive. The Player's Handbook says

Some feats have prerequisites. Your character must have the indicated ability score, class feature, feat, skill, base attack bonus, or other quality designated in order to select or use that feat. ... A character can’t use a feat if he or she has lost a prerequisite. (87)

The feat Nymph's Kiss has no prerequisites.

The DM can always house rule prerequisites for the feat, but if he doesn't, once the player's received the DM's permission and the player's character has taken the feat, the feat's there. Only if the character commits an evil act or is "in areas where magic is suppressed or negated (such as an antimagic field)" (PH 180) does the feat disappear.

Evil Acts

As the feat Nymph's Kiss is an exalted feat,

A character who willingly and willfully commits an evil act loses all benefits from all his exalted feats. She regains these benefits if she atones for her violations.... (BE 39)

Thus, if the character were "trying to dupe someone into buying a cursed item" (DMG 277), which is an evil act, all the character's exalted feats' benefits would be lost until he atoned.

Areas of Suppressed or Negated Magic

Strangely, a character loses all exalted feats in areas where magic doesn't function:

These [exalted] feats are... supernatural in nature (rather than being extraordinary abilities, as most feats are). (BE 39)

Luckily, the character with the feat Nymph's Kiss probably spent the skill points he gained, so he needn't subtract those when he enters such an area, but it's something to keep in mind if those feats are prerequisites.

Really, Talk to the DM

The DM must approve the feat, and he must be on board with your character taking a feat that mandates your character be good or lose the feat. If the DM's used to putting devastating moral quandaries in front of the characters, forcing them to constantly choose the lesser of several evils, the character will be hard to play and might not fit the campaign. That's a thing. Talk to the DM. Absolutely.

But only the DM can house rule that your character must do something to keep his feat. That's his call... even if the feat has no prerequisites.