The slang conviconvi is probably short for convidadoconvidado, meaning: someone who is invited to share something, treated to something; or maybe conviteconvite, which is a banquet or, by extension, the treat itself.
Based on the above, it makes sense that when someone says "sin convis" what they mean is "no invitees" or "no treats", i.e. they do not want to share.