No, but "we like having a band" or "we liked having a band". "We would like" would be gostaríamos, gostávamos
"We like to have a band" is a very awkward sentence in English. Imo it should be either "we would like to have a band" or "we want a band"
No, that would be something else (queremos ter uma banda). This means "we like having a band".
Because this course is made by Brazilians, they've been used to American textbooks which teach the construction "like to do" to the detriment of "like doing". It really is better to use the -ing form in English after "like", unless you're sure the meaning really calls for the "to" infinitive.
What would "band" mean in this context? A carnival band? A wristband? Something else entirely?
"We like having a band" and "we like to have a band" are both acceptable English as they are used in two different ways, and mean different things.
With that in mind, how do I write "we like to have a band" (which suggests that we don't have one now, but it won't last long if we have our way)?
="Nós gostaríamos de ter uma banda." if you mean 'we'd like to have a band.'. I was wondering if there is a way to express this difference you noticed in English (experience vs. anticipation), but I'm affraid it's not replicable in Portuguese in the same tense.
Not future, although that's correct. I meant it in a general sense. It would suggest they've had a band at times before and may not now.
"We don't have a band but still...we like to have one".
"Are you going to that amusement park yet again tonight"?
"Yeah...hey...we like to have fun". (Presumably fun isn't being had at the time, but it will...and still it's not a future statement).
Back when I first questioned this sentence I think I was looking for the continuous version of "ter", not knowing if it was an option or if it even existed.
Well, you can use the simple present tense of "gostar" (main verb) to the same idea in English. In your example: "Sim... Veja... Nós gostamos de ter diversão [por perto]." (I forced the use of "ter", a better way to say it is "...gostamos de nos divertir.").
You can also say: "Estamos gostando de ter uma banda." to highlight the experience at the moment of speaking.
But the continuous version of "ter", specifically, is used together with "ser/estar" and/or in another kind of sentences. E.g.:
"Estou tendo problemas com a banda." ('I am having problems with the band.')
"Gosto de bandas, tendo uma ou não." ('I like bands, having or not having one.')
Hopefully it could clarify the matter... :)