You can do it.
You have to escape them, but you just have to figure out how.
Google says for TF2 console you have to use double doublequotes ( "" )
In Gmod lua, you can use \", no idea if Gmod is same for console commands.
With Gmod, it could go either way, but I'd try "" first.
bind p "ulx tsaycolor ""message here red"" " (I've not studied this addon's command stucture, does red get included as part of the say string, or after, if after, place it after 'here')
Perhaps
bind p "ulx tsaycolor \"message here red\" "
And, even perhaps singlequotes.
bind p "ulx tsaycolor 'message here red' "