According to Christians who believe that we cannot pray to Jesus, are we allowed to communicate to Jesus via song?
Reason would seem to dictate that the answer would be no!
However many Christians sing and/or chant prayers, that are direct petitions to Jesus. These are not just simply songs of the praises of Jesus in honour of his miraculous works he preformed while on earth, they are actual prayer petitions.
Even In the 4th century, St. Augustine was inspired to state that “Singing is praying twice.” It’s an adaptation of a quotation usually attributed to St. Augustine, “One who sings prays twice.”
Historically speaking, Christians often petitioned Jesus in prayer through song in one form or another.
Here is just one example of an historical traditional use of public Catholic prayer which is often chanted as a devotional prayer: Litaniae Sanctissimi Nominis Iesu (Litany of the Most Holy Name of Jesus).
Iesu, Fili Dei vivi,
R. miserere nobis.
Iesu, splendor Patris,
R. miserere nobis.
Iesu, candor lucis aeternae,
R. miserere nobis.
Per mysterium sanctae Incarnationis tuae,
R. libera nos, Iesu.
Per nativitatem tuam,
R. libera nos, Iesu.
Per agoniam et passionem tuam,
R. libera nos, Iesu.
Iesu, audi nos.
R. Iesu, exaudi nos.
Oremus;
Domine Iesu Christe, qui dixisti: Petite et accipietis; quaerite et invenietis; pulsate et aperietur vobis; quaesumus, da nobis petentibus divinissimi tui amoris affectum, ut te toto corde, ore et opere diligamus et a tua numquam laude cessemus.
Sancti Nominis tui, Domine, timorem pariter et amorem fac nos habere perpetuum, quia numquam tua gubernatione destituis, quos in soliditate, tuae dilectionis instituis. Qui vivis et regnas in saecula saeculorum. Amen.
The complete litany, along with it’s English translation may be found here: Litaniae Sanctissimi Nominis Iesu. I deliberately quoted the the Latin text to help explain that the notion of prayer that is sung or chanted is traditional way of prayer that is several centuries old.
The Orthodox and Catholic Churches both chant the Kyrie eleison.
Kyrie, a transliteration of Greek Κύριε, vocative case of Κύριος (Kyrios), is a common name of an important prayer of Christian liturgy, also called the Kyrie eleison.
In the Bible
The prayer, "Kyrie, eleison," "Lord, have mercy" derives from a Biblical phrase. Greek ἐλέησόν με κύριε "have mercy on me, Lord" is the Septuagint translation of the phrase חָנֵּנִי יְהוָה found often in Psalms ( 6:2, 9:13, 31:9, 86:3, 123:3)
In the New Testament, the Greek phrase occurs three times in Matthew:
Matthew 15:22: the Canaanite woman cries out to Jesus, "Have mercy on me, O Lord, Son of David." (Ἐλέησόν με κύριε υἱὲ Δαβίδ)
Matthew 17:15: "Lord, have mercy on my son" (Κύριε ἐλέησόν μου τὸν υἱόν)
Matthew 20:30f, two unnamed blind men call out to Jesus, "Lord, have mercy on us, Son of David." (Ἐλέησον ἡμᾶς κύριε υἱὸς Δαβίδ)
In the Parable of the Publican and the Pharisee (Luke 18:9-14) the despised tax collector who cries out "Lord have mercy on me, a sinner" is contrasted with the smug Pharisee who believes he has no need for forgiveness.

Kyrie XI ("orbis factor")—a fairly ornamented setting of the Kyrie in Gregorian chant—from the Liber Usualis.

24 inspirational quotes about classical music: St. Augustine
Are Christians allowed to communicate to Jesus in the form of song, just as did the 24 elders? Absolutely.
According to the Ethiopian Orthodox Tewaido Church the twenty-four elder are Holy Angels (Seraphim).
The twenty-four Priests of heaven are a class of priestly angels positioned in the fifth rank of angelic hierarchy and perform priestly duties without rest. (Rev. 4:4, 10, 11)
The Ethiopian Orthodox Tewaido Church has been built churches dedicated to them and celebrates their feast each year on Hidar 24 (December 3).
They are saints with God and they make intercession on behalf of the race of men, and they bring unto Him the prayers of the saints like incense in the censers in their hands. Alms and oblations cannot ascend to God except through them even as Saint John the evangelist says in the Vision of the Apocalypse, “I saw the place of Twenty Four elders round about Him, and they were sitting on twenty four thrones; and on their heads were twenty four crowns, and in their hands were twenty four censers containing sweet-smelling incense, which is the prayers of the saints who dwell upon earth, and which they make to rise up before God, the Sustainer of the Universe.”
And he also says, “And I heard Four Beasts praising and saying, Holy, Holy, Holy, Lord [God] of Hosts, the heavens and the earth are filled full of the holiness of Thy glory”. And straightway the twenty four priests of heaven fell down with their faces to the ground, and they took off their crowns, and they said unto Him, Glory, and honor, and thanks are fitting for Thee. And when a command went forth from God they fell down again with their faces to the ground, saying, Glory, and power, and judgment, and righteousness belong to our God” (Rev. 4:4).
And because the father of the Church have found statements about these Twenty Four Priests of heaven in the Holy Scriptures, and have seen stories told of them by the Apostles and in their Canon, saying that they are nigh unto God, they have ordered and ruled, saying, “The name of him that celebrates their commemoration shall be revealed upon earth. And they shall entreat God on his behalf to forgive him all his sins.” Therefore, Church fathers tell the people to honor the festival of the commemoration of the Twenty Four Priests of heaven.
Salutation to you, O priests of the Law. Their intercession be with us and Glory be to our God forever. Amen
The Commemoration of the Festival of the Twenty four Priests of heaven
The following may be of interest: