NOTE: somehow I managed to include Nenya instead of Vilya... so while you can still keep dreaming of drawing Vilya, it won't happen with this deck list :)
Since the card pool is restricted to the Core set + starter deck, most staples in a standard Vilya deck are missing. Therefore, in order to get the ring as fast as possible on the table, several card draw options are included.
Another limiting factor compared to Vilya decks that use a complete card pool is the somewhat limited amount of high cost allies. But I resisted the temptation of including Brok.
Narvi's belt is not crucial, but it can be quite useful for resource smoothing in mid-game, to be able to play expensive allies from hand with Gloin's resource generation. Heir of Mardail works nicely with the resources generation of Gloin, Steward of Gondor and Magic ring. Since it's unique I decided to include two copies and two copies of Unexpected courage (more flexible, but cannot be played until Vilya is on the board).
Protector's of Lorien is a cheap option to boos willpower or defense when needed: with all the card draw it's not unlikely to have 10+ cards sitting in hand and doing nothing.
The number of allies could be somewhat increased, but I found it to be OK in some preliminary runs.
What's almost entirely missing is threat reduction. Elrond's counsel can be added to the pool, perhaps switching out the 2 Defenders of Ramnas and 1 protector of Lorien.