I am currently having issues with the multiplayer beta. I cant invite my friend on steam neither is there an invite code visible. We can't play together. Is it just me? Or you have the same issue? (We both have good internet connection.)
I'm also having this issue! My game doesn't show up automatically, and I cannot invite them to the game, nor can they join. We're playing in the same room.
Double check that Steam is running, that it is not in Offline Mode, and that no other computers are signed into the same Steam account.
My husband and I haven't had any issues with this - he goes into the settings option within the game and selects the option to invite other players, which brings up his Steam friends list and he can click on me to invite me. We've never used an invite code, but it does require my friends list setting to show online for it to work.
I've experienced something like this with my partner - the problem only occurred when steam wanted to update her Beta version though. If you go to the invite section of your co-op screen and there is only a LAN option then steam is updating your game (or so we have experienced) so just exit the game, give it 5 minutes and start again. Hope this helps!