The noun Spy Wednesday denotes the Wednesday before Easter.

This noun refers to the day on which Judas Iscariot formed the intent to betray Jesus—as explained by a person signing themself ‘Cleric’ in The West-End Querist, published in The Westminster and Chelsea News (London, England) of Saturday 13^th August 1881:

Spy Wednesday—This is the Wednesday coming before Good Friday, and the day on which Judas Iscariot concerted with the Jewish Sanhedrim to betray the Saviour for thirty pieces of silver.

Here, ‘Cleric’ quoted the gospel of Matthew, 26:14-16, which is as follows in the King James Version (1611):

14 Then one of the twelue, called Iudas Iscariot, went vnto the chiefe Priests,
15 And said vnto them, What will ye giue me, and I will deliuer him vnto you? and they couenanted with him for thirtie pieces of siluer.
16 And from that time he sought opportunitie to betray him.

In Spy Wednesday, therefore, the noun spy is used in the acceptation of one who spies upon, or watches, a person or persons secretly—because, from Wednesday onwards, Judas Iscariot secretly sought an opportunity to deliver Jesus to the Jewish authorities.

The earliest occurrences of Spy Wednesday that I have found indicate that this noun originated in Ireland:

1-: From Quarter Sessions, published in Saunders’s News-Letter, and Daily Advertiser (Dublin, County Dublin, Ireland) of Thursday 6^th July 1809:

John Rogers was indicted for stealing iron, the property of Michael Bryan, in the month of March last. The first witness produced was Michael M’Grath, who deposed that he lives in Cullen’s Wood; that on Spy Wednesday night last, a jaunting car was stolen, the property of Michael Bryan.

2-: From the “Pastoral Address of his Grace the Archbishop of Tuam to his Clergy, on the occasion of the commencement of Lent”, published in several Irish newspapers on Saturday 7^th March 1835—for example in the Kilkenny Journal, and Leinster Commercial and Literary Advertiser (Kilkenny, County Kilkenny, Ireland):

Dear and Beloved Brethren.—We are about to enter into that holy season which has been set apart, from the time of the Apostles, for the salutary exercises of penance. This is the acceptable time in which fasting and other mortifications of the flesh are more particularly prescribed, in order that through the merits of the Redeemer they may be the means of securing to us the divine mercy. […]
During, then, the penitential period of Lent, one meal only, with a slender collation, is allowed to those who are not engaged in hard labour, or who are not comprehended in those classes, who, by reason of age or other infirmities, are exempted from fasting. The use of flesh meat is prohibited during the entire of the Lent—the use of eggs is not permitted on Fridays, or during the first and last weeks of this penitential time. On Ash Wednesday and Spy Wednesday and Good Friday, even milk and butter are not allowed to the faithful.

3-: From Holy Week in Rome. From a Correspondent of the Freeman’s Journal, published in the Kilkenny Journal, and Leinster Commercial and Literary Advertiser (Kilkenny, County Kilkenny, Ireland) of Saturday 9^th May 1835:

Spy Wednesday.
On this day I presented myself at the sistine, at a few minutes before four o’clock in the evening, to hear the Lamentations of Jeremiah and the Miserere chaunted.

4-: From the “regulations for Lent, signed by the Right Rev. Dr. Ryan, Roman Catholic Bishop of Limerick”, published in The Clare Journal, and Ennis Advertiser (Ennis, County Clare, Ireland) of Thursday 18^th February 1836:

Milk and butter are forbidden on Ash Wednesday, Spy Wednesday, and Good Friday.

5-: From the “Instructions and Regulations addressed to the Roman Catholic Clergy and Laity of the Diocese of Limerick, […] by order of the Right Rev. Dr. Ryan”, published in The Kilkenny Journal, and Leinster Commercial and Literary Advertiser (Kilkenny, County Kilkenny, Ireland) of Wednesday 7^th March 1838:

Milk and butter are forbidden on Ash Wednesday, Spy Wednesday and Good Friday.

6-: From The Most Rev. Dr. Machale’s Circular to his Clergy, published in The Weekly Waterford Chronicle (Waterford, County Waterford, Ireland) of Saturday 23^rd February 1839:

It would be our sincere wish to revert to the holy and primitive practice of total abstinence from flesh meat during the coming forty days, and we do not despair but the piety of the people will be yet anxious for its observance.— The late destructive storm, which should be an incentive to penance, inasmuch as it was an instrument of the wrath of the Almighty, has thrown many out of the shelter of a home, and reduced them to great destitution. We therefore, in the ardent hope that the rich and affluent may be induced, on account of this indulgence, to open the bowels of mercy more abundantly to the poor, adopt the same regulations as to Lent which we published for the last three seasons; allowing flesh meat on all days except Wednesdays, Fridays, and Saturdays, the entire of the last week, and the first from Ash-Wednesday, inclusive. During the last and the aforesaid portion of the first week eggs are prohibited, as also on Fridays. No sort of milk diet, known by the name of “lacticinia,” is allowed on Ash-Wednesday, Spy-Wednesday, or Good-Friday; nor are flesh and fish permitted on any day during the same meal.