"He gave her a ring while proposing her for marriage."
This sentence feels long winded. I am sure there's a more idiomatic way to say this. Is there? I am looking for an idiom a native speaker may use.
"He gave her a ring to propose her for marriage."
"He gave her a ring while bending the knee for a marriage proposal."
All these sentences sound unnatural.
Both your first and second versions are not idiomatic, at least not in US English.
He gave her a ring while proposing marriage
He gave her a ring while proposing marriage to her
are idiomatic although awkward. What is being proposed, that is suggested, is a marriage.
Your third skews a stock phrase that is archaic in form, "on bended knee." Because it is a stock phrase, altering it sounds odd.
Some of what sounds natural relates to modern conventions involving proposals of marriage in the U.S. In a usual situation, a man offers to give a ring to a woman if she agrees to marry him; the offer and acceptance are a ceremony patterned on the old Latin phrase Do ut des: I give so that you will give. The gift is not technically made until she accepts the proposal of marriage, or, perhaps more realistically, her acceptance of the ring represents acceptance of the proposed marriage, and taking physical possession of the ring is almost always accompanied by overt words of assent to the proposed marriage.
Thus, what are more characteristic are
He proposed
He proposed by offering her an engagement ring
He proposed marriage
He proposed marriage by offering her an engagement ring
He offered her an engagement ring to propose
He offered her an engagement ring to propose marriage
On bended knee, he proposed
On bended knee, he offered her an engagement ring
Often times instead of saying "proposing marriage" the phrase "pop the question" is used. The question being referenced is, "Will you marry me"
So if you're looking for an idiomatic way of saying that he gave the ring while proposing marriage, you could say:
"He gave her the ring while he popped the question."
This does presuppose that marriage is already being discussed in the story. Without that context, "popping the question" would sound a bit out of place.
The first problem with "propose her for marriage" is that it does not mean what you are trying to say. To propose someone or something is to offer him or it as a candidate. For example:
I proposed Jane for the job of director.
or
I proposed adhesive tape as a temporary repair.
So the sentence:
John proposed Jane for marriage.
probably means that John has a friend who wants to marry. John tells his friend that he should consider marrying Jane.
Even if these were the circumstances, you would not say it this way. Putting "for marriage" at the end makes it sound like a clarification. John seems to be hinting to his friend that though some girls can be bedded without marrying them first, Jane is not one of them. She is "for marriage". It would be much better to say:
John proposed he marry Jane.
But all this is beside the point because what you are trying to say is:
John proposed marriage to Jane.
Note that John proposes marriage. He does not propose Jane. He proposes marriage to Jane.
