What organizations give computer science PhD students travel grants?

I'm not sure this helps in exactly your case but you could give it a try: http://www.scholarshipportal.eu/

I would shift the "focus" of the travel grant search from "PhD" to "Computer Science," and find out which "computer science" organizations can help you.

As a PhD candidate, you represent what is "fresh" in the field. Thus, you have something to offer to more experienced practitioners (or, for that matter, to undergraduate students). I would look for situations to "work" your way through (as a speaker, tutor, assistant, etc.). It's a lucrative field, and many people would probably be willing to "pay" for your expertise in the form a travel budget, or other ways.

PhDs in many other fields (e.g. history or liberal arts), probably don't have this advantage.

Most Computer Science conferences I've attended have some sort of student travel grant program. Most ACM-sponsored conferences have them. There are also a number of endowed funds through the IEEE that give travel grants. The Computing Research Association also provides generic travel grants specifically designed for female Ph.D. students in Computer Science. They may also have travel grants for men; I am not sure.

These grants subsidize (or sometimes even fully cover) the student's travel expenses, usually in return for the student working for some amount of time (e.g., manning the registration table, organizing poster sessions, providing technical assistance and/or moderation during technical sessions, &c.). Some grants require that you are also presenting a talk at the conference, others do not.

A number of conferences in your field may provide travel grants to the conference, be sure to check around the website as they're often hidden. Other places to check:

1. Your university. Many offer one-time or the like travel grants to graduate students.
2. If its for field work - though I have a hard time imagining what that might be for computer science, many small grants that graduate students are eligible to apply for will allow you to spend some of the money on travel.