I'm thinking that a houseguest who stays on your couch should be something like hospes lectuli. But that sounds more like a guest invited by your couch, which is silly. In my non-expert understanding of how Latin normally works, this kind of construction should call for an adjective. But all I know is the noun lectulus. How could I make that into an adjective so that it clearly modifies hospes?
You could use lectualis or lectuarius, "of or belonging to the bed". Lewis & Short:
lectŭālis, e, adj. [2. lectus], of or belonging to the bed: "morbus", which confines one to his bed, Spart. Hadr. 23 dub. (al. letalis).
lectŭārĭus, a, um, adj. [id.], of or belonging to the bed, bed- (late Lat.): "lectuaria (lecticaria) sindon", Non. 537, 21.
But, in this case, perhaps an adjective from a verb might be your best option, like the participle pernoctans, from pernocto "stay the night".
P.S. Using a noun in the genitive is usually a very natural option in Latin, so I think lecti would be a good choice. The genitive can be used to express many other relations than real possession; it can also express a vague relationship like "belonging to, having to do with".
In your question you have used the genitive, and 'lecti' of a bed may be your best option. Or 'lectuli.'
It's almost impossible to find an adjective from any of the words for bed; and those two which can form adjectives imply the guest is sick or in child-birth. Lectus, torus, cubile, stratum (often in plural) or even clinus, tectus and grabatus.
contubernalis, a couch fellow.
sounded promising, but it's the (ten) men who shared a tent in the army.
In general, adjectives from nouns are difficult; it is much easier to form adjectives from verbs:
cubans: present participle of cubo: lie down,
Hospitality is best expressed by:
Hospitio aliquem excipere where 'aliquem' stands for any guest.
If you want something more literally similar to English, here is a suggestion. I want to get an adjective derived from "couch" and a noun for "surfer", as I find that to be the best Latin equivalent of English noun adjuncts.
A couple of words for a couch come to mind after consulting dictionaries: lectus, lectulus, torus, stibadium, grabatus, grabatulus. If you want to refer to someone who comes to sleep on your couch rather than in your bed, I would avoid the ones that also stand for a bed (lectus, lectulus, grabatus). I think torus is also way too general and hard to parse as a couch. The least prone to misunderstanding seems to be stibadium, a seat or a couch.
I don't think we should be trying to translate "surfer" in a way that connects to surfing; I am not aware of a Latin word for it, and it would lead to quite a confusing result. I would be badly confused with the English term "couch surfer" too if I had not heard it before. There are many different directions to go: hospes (guest), amicus (friend), viator (traveller). If this is a person who travels the world and sleeps on sofas, then I think viator works best. If the point of view is that of a couch-owner, then perhaps hospes.
So my suggestion would be viator/hospes stibadialis, depending on the point of view. If you use this, be prepared for your audience needing to take some time to parse it unless you introduce it well. In a suitable contest this would make a decent expression.