Sorry...I meant to add this, but clicked toe 'post' button too soon.
You may not need to use a syringe if your dog is happy to lick small amounts of the liquid from a dish. Just make sure you give a tiny amount each time, and wait maybe 10 minutes before giving another one....etc
Don't let your dog gulp water in the meantime. Only give the small amounts of liquid.
I really can't say for sure what might be causing this. Have you spoken to your vet about it?
One thing is for sure. Your dog needs water, or is going to become seriously dehydrated. If it has just started happening, and has been going on for 2 days, then my advice is to get your dog to a vet because there is a cause for the vomiting, and it can't go on.
Has this just started, or has it been going on for a long time?
If you have some time to wait for your vet appointment, then my advice is to give your dog unflavoured Pedialyte (if you can buy it) and if not, use water in which a very small amount of honey or maple syrup has been dissolved. You may need to start with warm water for this, and allow it to cool when the honey has dissolved.
Then using a syringe with NO NEEDLE! or a small plastic (not glass) turkey baster syringe a very small amount in the side of your dog's mouth. Maybe a teaspoonful or less each time. And keep that up as often as you can. Very small amounts each time.
Very small amounts have a better chance of staying down.
Try that -but it's just to prevent dehydration while you are waiting to see the vet.