Serait-ce possible.. is definitely correct¹. Unfortunately, Duolingo is well known for exhibiting this kind of mistakes.

Unlike Stack Exchange sites which allow almost anyone to correct questions and answers, Duolingo unflexible management policy is leading to such annoying inaccurate judgments.

Reporting them in the comment section is like talking to a wall. I gave up using Duolingo after being hit several times by such a stubborn attitude.

I just found the Duolingo comments related to that question and it reads:

— Shouldn’t "Ce serait possible…" be OK?
— Technically no. Only "Il" can be used as the impersonal. In every day’s life though, you could hear pretty often : "Ce serait possible de…"

One might conclude Duolingo is not teaching everyday’s French here, or at least is confusing correctness and language registers. Gilles’ excellent indepth analysis is explaining why serait-ce possible de… is unexpected and can be considered formally incorrect. Using subject-verb inversion (serait-il) is a formal way to ask a question while the non-inverted form (il serait/ce serait/ça serait) is colloquial/spoken French. By mixing formality (inversion) and relaxed register (ce), this form is rare. Note also that both serait-ça possible de… and serait-cela possible de… are never used.

¹ _{Or at least is something perfectly understandable, that doesn’t hurt most French native ears outside some grammar nazis, that you can find in a few printed material (although serait-il possible de is much more common), that you can read in online forums. Not using il in a similar construction is even present in Marcel Proust’s Le côté de Guermantes: Serait-ce possible que je vous fisse chercher le soir quand je serai libre ?}

I’m going to side with Duolingo here. “Serait-ce” in this particular sentence is not horribly wrong, it’s something a French person could say, but it sounds a bit weird and I think it’s formally incorrect.

Ce is the correct pronoun to refer to a previously mentioned object or concept when the pronoun is the subject of the verb être. Il is usually incorrect in this particular case. So “Serait-ce possible ?”, as a full sentence asking whether something that was previously mentioned is possible, is correct. However “Serait-il possible de … ?” is different: here the subject pronoun does not refer to something that was previously mentioned. Instead, the subject pronoun is there because French absolutely requires a subject. And in that case, the pronoun is il, even with the verb être.

“Serait-il/ce” is the formal way of asking a question. At this level of formality, you can’t deviate much from formal grammar. I don’t find ”Serait-ce possible de … ?“ idiomatic at all. On the other hand, with the medium-formality way of asking questions, I think “Est-ce que ce serait possible de … ?” sounds more natural than “Est-ce qu’il serait possible de … ?”, which sounds a bit formal. “Est-ce que ça serait possible de … ?” is also possible and sounds more informal. With the informal way of asking questions, “Ça serait possible de … ?” is the most natural pronoun, “Ce serait possible de … ?” is ok but slightly weird, and “Il serait possible de … ?” is not idiomatic due to mixing formality levels.

Looking at written usage, “Serait-il possible” beats “Serait-ce possible” by a wide margin, but less so over time. If you look at occurrences of “serait-ce possible”, there is almost never a complement: the pronoun ce refers to something that was mentioned previously, in which case it’s the grammatically correct pronoun. When the subject pronoun is a grammatical subject with the semantic subject coming after the verb group and introduced by de (+ noun) or que (+ verbal phrase), the pronoun is almost always il, not ce. There is some usage of “serait-ce possible de …” and “serait-ce possible que …”, but not much, and (especially with de) usually in dialog.