There aren't any verses in the Bible that say "go vegan!" but there are many that should help you convince people that Christianity and veganism are not mutually exclusive. I get that argument all the time too, and I think the problem is the misinterpretation of the word "dominion." People think it means domination or control, when really it means that we were given the responsibility of them...we were entrusted by God to care for them. That said, I have a few verses that I can pass along to you that may help.
Here are some that I like to reference:
"Then God said, "I give you every seed-bearing plant on the face of the whole earth and every tree that has fruit with seed in it. They will be yours for food. 30 And to all the beasts of the earth and all the birds of the air and all the creatures that move on the ground—everything that has the breath of life in it—I give every green plant for food." And it was so."
That one is so good it speaks for itself!!
"Then God blessed Noah and his sons, saying to them, "Be fruitful and increase in number and fill the earth. The fear and dread of you will fall upon all the beasts of the earth and all the birds of the air, upon every creature that moves along the ground, and upon all the fish of the sea; they are given into your hands. Everything that lives and moves will be food for you. Just as I gave you the green plants, I now give you everything.
"But you must not eat meat that has its lifeblood still in it. 5 And for your lifeblood I will surely demand an accounting. I will demand an accounting from every animal. And from each man, too, I will demand an accounting for the life of his fellow man."
This is God giving us permission to eat meat, but it certainly doesn't say that we have to! He only gave man permission to eat meat AFTER the flood, when there was no vegetation for Noah and his family to eat. Permission was given because the people could not survive without it....that did NOT give us permission to factory farm and abuse the gifts God has provided!
"He who regards one day as special, does so to the Lord. He who eats meat, eats to the Lord, for he gives thanks to God; and he who abstains, does so to the Lord and gives thanks to God."
This verse is saying that it doesn't matter whether you do or do not eat meat, so long as you do it in thanks.
"Do not destroy the work of God for the sake of food. All food is clean, but it is wrong for a man to eat anything that causes someone else to stumble. It is better not to eat meat or drink wine or to do anything else that will cause your brother to fall."
I think that one is interesting...because by eating meat you are aiding in the cruel actions of others in most cases.
Here is my favorite:
"Blessed are the merciful, for they will be shown mercy."
I think that kind of sums it up, don't you?
By the way, all of these verses are NIV.
EDIT: I also wanted to add that you should be careful to know the context of verses that you quote to others. If the verse itself SOUNDS like it fits, it still may not...the surrounding verses will give you an idea of what the verse is intended to mean. If you start taking things out of context you'll end up sounding like you don't know what you're talking about.
I'm a Christian and a vegan....and I don't think two things could go together better :)