Author Notes: This section has a slightly more literal translation, information on the mutations and a few miscellaneous notes. At the end are the sources I used in the translation.

Disclaimer: The names of the Valar belong to Tolkien. The ceremony is traditional Celtic with changes made by me to fit into Tolkien's mythology.

Grammatical Notes

We call Manwë, Lord of the Breath of Arda. Listen to this oath.
Estam Vanwë, Aran e-Thûl Gardh. Lasto nan-gwaedh hen.

Vanwë - lenited form of Manwë
e-Thûl - mixed mutation of en Thûl
nan-gwaedh hen - (lit. 'the oath this'), hen is the lenited form of sen.

We call Varda, Lady of the Stars. Listen to this oath.
Estam Varda, Rîs en Elin. Lasto nan-gwaedh hen.

We call Ulmo, Lord of the Waters. Listen to this oath.
Estam Ulmo, Aran en-Nîn. Lasto nan-gwaedh hen.

We call upon Yavanna, Queen of the Earth. Listen to this oath.
Estam Yavanna, Rîs e-Cae. Lasto nan-gwaedh hen.

Cae - This should be Gae - see note at the end of the first chapter.

As seed and root, as bud and stem,
Be eredh a holch, be duiw a delch,

holch - lenited form of solch
duiw - lenited form of tuiw
delch - lenited form of telch

as leaf and flower, as star-fading and star-opening, as life and as love,
be lass a loth, be vinuial a aduial, be guil a be vîl,

vinuial - lenited form of minuial
guil - lenited form of cuil
vîl - lenited form of mîl

in the sight of Eru, thee I bring to my hand, my heart and my soul,
ned i gened Eru, le tegin na gamen, 'uren a faeren.

gened - lenited form of cened
le - Quenya 'thee', but used in Sindarin (ref. LOTR, 'A Elbereth Gilthoniel', p 231, pub. Houghton Mifflin)
gamen - lenited form of camen
'uren - lenited form of guren

And death shall not cleave us,
A gûr law ristatha ven,

ven - lenited form of men

as in Aman again we shall meet,
be ned Aman ad geveditham,

and know, and have remembrance and desire.
a istatham, a geritham rîn a anírad.

anírad - gerund form of the verb aníro (lit. 'desiring')

I give you this ring as an oath of my love of you.
Annan le i gorma hen be 'west o mîlen le

i gorma hen - lit. 'the ring this'. gorma is the lenited form of corma (Quenya), and hen is the lenited form of sen.
'west - lenited form of gwest

May the ring tell always
Narn i gorma aen ui

of my eternal love.
o mîlen uireb.

My loving bride / bridegroom, to thee I bind myself.
Dineth / Daer vilui nîn, al le gwedhin im.

vilui - lenited form of milui
al le - nasal mutation of an le

With this ring, I give thee my heart, my body and the breath of my soul.
Ah i gorma hen, annan le 'uren, thrawen a i thûl faeren.

i gorma hen - (lit. 'the ring this'), gorma is the lenited form of corma, hen is the lenited form of sen.
'uren - lenited form of guren
thrawen - lenited form of rhawen

O Valar, make firm this union between Children of Eru.
A Valar! Tangado i erthad hen im Hîn Eru.

i erthad hen - (lit. 'the union this'), hen is the lenited form of sen.

Watch over them, lead them and protect them. Your blessings give to their household
Tiro den, togo den a berio den. 'Alu lîn anno a cherth dîn

den - lenited form of ten
'Alu - lenited form of Galu (as the direct object of 'give')
a cherth - nasal mutation of an herth
dîn - lenited form of tîn

and to the children born of their union.
a nan-hîn ennin o erthad dîn.

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Sources
Some of these sources contradict one another, so I've done my best to figure out what seems most correct.

Ryszard Derdzinski, Summary of the Sindarin Grammar: www.elvish.org/gwaith/language.htm

Helge Fauskanger, Sindarin - The Noble Tongue: move.to/ardalambion

Helge Fauskanger, Suggested Conjugation of all known or inferred Sindarin verbs: move.to/ardalambion

J. R. R. Tolkien, The Lost Road, 'Etymologies', pub. Ballantine/Del Rey

Didier Willis, Hiswelókë, The Sindarin Dictionary Project: www.geocities.com/almacq.geo/sindar/index.html