First of all I'm asking this question. Because, I had always pronounced the name Jesus a little different than the way I was corrected by my niece a couple days ago. Therefore, I would like to get the right way of saying this once for all.
Well here is what I had always said: "sheezus"
Close to the English pronunciation, but the initial consonant is wrong; it is /d͡ʒ/ not your /ʃ/.
Here is what she told me to say: "geesoos"
Is this /d͡ʒisus/? If it is, it's incorrect.
Here is what I found on Cambridge Dictionary: "dʒizəs" which I think it sound close to the way I used to say it but my listening is not perfect though. ):
This pronunciation applies to the religious figure only.
Let's actually tackle your question:
Ok, well. Since my first language is Spanish I looked up for the way to prounciate it in Spanish and this is what I found: "yisus" which is the same as my niece told me. Below is the link for a Yahoo answer where they say "yisus" is the right way of saying Jesus.
The problem here is that Spanish has no d͡ʒ. It does have ʝ which is spelled as Y there, hence it being transcribed "yisus". In addition, Spanish has no /z/ phoneme, hence the "s" where /z/ should go. Given your transcription of your own pronunciation, I think you already know how to make a /z/ sound.
The schwa (it's the U in "Jesus"), is a different problem which has been tackled to death a million times already. Just Google it.
By the way, this is /d͡ʒ/.
A big catch: The religious figure Jesus, and Spanish-speaking people named Jesus are pronounced very differently in English.
Jesus of Nazareth: /d͡ʒiːzəs/. The name of the son of God has been Anglicized.
Spanish-speaking people called Jesus: /heɪsus/. This is to approximate Spanish /xesus/.