I'm about to bottle my first Coopers home brew and I don't have a rapid bottler. Can I pour it straight from the tap or will I have problems?
The bottling wand that comes in the Cooper's kit is there to make bottling easier & doesn't add any special technique required for the process. If you do pour straight from the tap, unless you're careful, you'll find it hard to fill the bottles to consistent / accurate levels, you will likely make a huge mess and you could waste precious beer.
I'd recommend holding out an extra day & visiting your local homebrew store to pick one up (they're under $10 where I live) but as long as you're careful, you could get away with bottling straight out of the tap.
For more info, have a read of "How To Brew" - Section 1, Chapter 11 covers priming & bottling.
I assume you mean a tap on your fermentor/bottling bucket and not a tap like from a kegging system.
The biggest problem is getting too much air/oxygen into the beer. You can fill that way, but the beer will potentially stale faster because of the oxygen pick up. At least get a piece of tubing that will reach from the "tap" to the bottom of the bottle. Fill slowly and when you pull the bottle off the tubing you should have about the right amount of head space.