Two questions here: can you have a multi-publisher subscription, and can you have a "subject-specific" subscription?
For the first, I suspect the most likely answer is "you can't". I'm not aware of any service (either for institutions or individuals) that offers a subscription with an arbitrarily selected set of journals from across multiple publishers. Generally speaking, you'd have to set this up with each publisher.
For an institution, you can get close to a single subscription model by using a subscription agent, who will handle the details of your subscriptions for you and send you one invoice, but even then it's still potentially quite a lot of work to actually get each one working, and - as we saw with Swets last year - no guarantee it'll be a stable solution long term. I don't know if similar services are available for individuals; I've certainly never noticed them advertised.
On the second question - more or less, yes. The publishers usually offer three approaches to subscribing - a manually selected list of journals ("I want A, and B, and C..."); thematic packages (Elsevier, for example, has relatively broad "subject collections"), or an everything-included deal, which isn't much use for you. The first option is usually more expensive if you want a large range of titles.
Using the thematic packages, you probably could just get computer science journals - but this might be quite loosely defined. (Elsevier's set includes, for example, the Journal of Rail Transport Planning & Management!)