Try, Keep Thou my Way by Fanny Crosby.

No, it's more direct than that.
I think its starts:

"Gladly the Cross I'd bear,
For him that diddly diddly dum"

(e.g. "for him that sits upon the throne")

This may or may not be it (although it's almost certainly the inspiration for "Gladly, The Cross Eyed Bear" )

It's a hymn called "Keep Thou My Way", words by Fanny Crosby, music by Theodore E. Perkins:

1.
Keep Thou my way, O Lord, Be Thou ever nigh;
Strong is Thy mighty arm, Weak and frail am I;
Thou, my unchanging Friend, on Thee my hopes depend;
Till life's brief day shall end, Be Thou ever nigh.

2.
Keep Thou my heart, O Lord, Ever close to Thee;
Safe in Thine arms of love, Shall my refuge be;
Then, o'er a tranquil tide, My bark shall safely glide;
I shall be satisfied, Ever close to Thee.

3.
Keep Thou my all, O Lord, Hide my life in Thine;
O let Thy sacred light O'er my pathway shine;
Kept by Thy tender care, Gladly the cross I'll bear
Hear Thou and grant my pray'r, Hide my life in Thine.

Hope it helps

God bless,
Steve

This is not listed on the CCLI page, nor the Cyber Hymnal, which is the outstanding source online for hymns nor in my small collection of hymnals. In fact, all I could find are the old jokes about the hymn being confused by small children as "Gladly the cross-eyed bear", or also known as "Gladly my cross I'd bear".

Need to find the lyrics of this hymn for a member of our Church Congration who has promised to donate money to Christian Aid if the lyrics can be found. I believe a line is "Gladly the Cross I'd bear for Jesus". Please email me at [email][email protected].[/email] Many thanks. Angharad