I found this possibility expressed profoundly in Psalm 138:
I will praise you, O LORD, with all my heart;
before the "gods" I will sing your praise.
I will bow down toward your holy temple
and will praise your name
for your love and your faithfulness,
for you have exalted above all things
your name and your word.
When I called, you answered me;
you made me bold and stouthearted.
May all the kings of the earth praise you, O LORD,
when they hear the words of your mouth.
May they sing of the ways of the LORD,
for the glory of the LORD is great.
Though the LORD is on high, he looks upon the lowly,
but the proud he knows from afar.
Though I walk in the midst of trouble,
you preserve my life;
you stretch out your hand against the anger of my foes,
with your right hand you save me.
The LORD will fulfill his purpose for me;
your love, O LORD, endures forever—
do not abandon the works of your hands.
This psalm is very overtly about the psalmist's faith in a truly faithful God. It introduces itself with the explicit praise of God's "love and faithfulness" and proceeds to quantify that faithfulness throughout. When he called, God answered. Though he is lowly, God is with him. When he walked in the midst of trouble, God preserved him. God will fulfill His purpose for him because His love will endure. Throughout you see no expression of doubt, only the constant affirmation of God's great works and the response in faith of the psalmist. In view of God's faithfulness, he will praise Him. He will bow down in the temple. He even invites all the kings of the earth to join in. God is faithful and worthy of our faith in Him.
It is jarring, to say the least, to conclude as he does. After affirming in so many ways that God has not and will not abandon him, the psalmist still cries out ironically from his unbelief: "Do not abandon me!" Here faith does not preclude doubt, but allows doubt to find its expression in the framework of this faith. "God, I know you are faithful. Please be faithful." It permits the tension which is always in us to find voice before a God who understands our frailty.
Authentic faith does not necessarily preclude doubt, but it always gives us a context in which to voice our doubt before God. We ought to find comfort in that freedom.