i haven't used oil because of the smell and it takes ages to dry. acrylic is definately what you want to stick to for the use you're talking about. i use water, flow enhancer, matte medim, or glaze to mix with my acrylics, depending on what i want to do with them. you might try mixing a little less water so they are just slightly soupy or use a liquid matte medium. i've also used gum arabic with my acrylics, which is intended to be mixed with watercolors, but i find it creates and interesting mix with the acrylic. i assume it's ok, because they are both water-based paints.
there is an easier answer though, if you want to drip your paint...buy some liquid acrylics or inks. they usually come with a dropper right in the bottle, so you even have some control over how much comes out. liquid acrylics are a little more expensive, but in my opinion definately worth it! i just started using them not long ago, after a suggestion from ann baldwin and i am so glad i did! you can extend them too to make them go farther.
by the way, what kind of paint are you using? and how much water did you mix? what is the end result you are looking for? how did you apply it to your canvas? i'm just trying to get a feel for the look and style you're going for.