I added "and Lady" in the third line of the first verse where "I go" is and you have to stretch the syllables, but I think the meaning is preserved. Once I included the Lady by name, I used "They" and "Their" to take the one syllable position of "God" and "God's".
There is an hour of peace and rest,
Unmarred by earthly care;
’Tis when before the Lord and Lady
I kneel in secret prayer.
The straight and narrow way to heav’n,
Where angels bright and fair
Are singing to Their praise, is found
Thru constant secret prayer.
When sailing on life’s stormy sea,
’Mid billows of despair,
’Tis solace to my soul to know
They hear my secret prayer.
When thorns are strewn along my path,
And foes my feet ensnare,
My Savior to my aid will come,
If sought in secret prayer.
May my heart be turned to pray,
Pray in secret day by day,
That this boon to mortals giv’n
May unite my soul with heav’n.