chean: I've had the "You can not trade with <person's name>" error on occasion; when it occurred using a web browser, trading worked again after logging out/clearing all Steam cookies etc. When it occurred in the Steam client, trading worked again after simply quitting and restarting the client. Apparently it's a fairly common error; IIRC I found those suggested fixes in some forum thread about it.
I tried logging out completely and exiting the client and also logging out of the website on both accounts, then logging back in. I had to do it twice but was finally able to accept a trade, thanks for the tip. Today when I woke up I tried to trade some items between my two accounts using different web browsers on the same computer and got the error again. I logged out of both, then re-logged back in and it worked the second time. Perhaps Steam is just being finicky about financial or trading transactions on computers/clients that have been left logged in and idle for some period of time or something like that, to protect someone against their computer being used by someone else.
In the end though I finally got it to work, so thanks for the tips!