I have been a CS professor at both large and small schools, so let me say a bit about getting into the program from both perspectives.
When I was working at a small school, we didn't have a large graduate population, so we accepted anyone who was qualified - regardless of research experience, etc. Anybody who was well-qualified (eg good grades and reasonable application package) also received a TAships covering the full cost of their degree. I still managed to get some fantastic students through this process. (Who didn't have research experience or were not from a traditional CS background.)
I am currently at a larger school, and we get something like 5x more applications than we are able to accept. So, most students get rejected, even highly qualified ones.
Based on this comparison, I'd suggest that you may need to look at a smaller school. Try to find an opening to work on a problem that might help you with a grad school application in the future.
In particular:
Find smaller schools with professors doing work in the area that you are interested in. Smaller schools can have very strong professors for many reasons. (Look particularly for recent publication activity.)
Read all of their recent papers.
E-mail ask research questions about their work. These questions should be genuine and should reflect a strong understanding of the work. You could even, for instance, ask if a project would be a suitable extension of the published work. (eg your method X works under conditions Y and Z. Would method W broaden the applicability of the approach? Or, would method V improve the performance when condition U also holds?)
Implement and try some of these ideas in practice. (You could even do this before doing #3.)
Use this to improve your graduate application. There are several ways to do this. First, if you have good communication with a professor, they may directly be able to help you get admitted to the program. But, this can also be part of your statement of purpose (SOP). I've read lots of awful SOPs. Your application will stand out if you can talk about a research problem you are interested in, why it interests you, and why it is a fit with the department/professors.
There are lots of variations on this approach, but I've had students use parts of the approach on me, and it worked.