tl;dr: Yes, there are: Merklebased, RSAorclassgroup based and latticebased ones.
$$ \def\Adv{\mathcal{A}} \def\Badv{\mathcal{B}} \def\vect#1{\mathbf{#1}} $$
RSA accumulators over class groups
Practically, the only (somewhatfast) accumulators without trusted setup (and constantsized proofs) are RSA accumulators^{1} instantiated with great care^{2} over class groups^{3}.
Merklebased accumulators
Theoretically đ, if you relax your definition of âaccumulatorsâ by:
 Removing quasicommutativity^{1}.
 Allowing for logarithmicallysized proofs (instead of constantsized proofs)
âŠthen, naturally you can use a Merkle prefix tree (a.k.a., a Merkle trie) to represent a set and obtain an accumulator.
Another approach is to either use (1) a binary search tree or (2) a tree with sorted leaves, where each internal node stores the minimum and the maximum element in its subtree^{4}.
Similarly, you can also use the rather beautiful Utreexo construction^{5}, which is also Merklebased but does not support nonmembership proofs.
Latticebased accumulators
Even more theoretically đ, assuming you donât care about performance at all, you might use a latticebased accumulator^{6},^{7},^{8},^{9}. Some of them do not need a trusted setup, like ^{6}.
Even better, the recent latticebased vector commitments by Peikert et al.^{10} can be turned into an accumulator. (Interestingly, I think accumulator proof sizes here could be made âalmostâ $O(\log_k{n})$sized, for arbitrary $k$, if one used their latticebased Verkle construction which, AFAICT, requires a trusted setup.)
RSA moduli of unknown complete factorization (UFOs)
One last theoretical idea is to generate an RSA group with a modulus $N$ of unknown factorization using the âRSA UFOâ technique by Sander^{11}. Unfortunatly, such $N$ are too large and kill performance. Specifically, instead of the typical 2048bit or 4096bit, RSA UFO $N$âs are hundreds of thousands of bits (or larger?). Improving this would be a great avenue for future work.

OneWay Accumulators: A Decentralized Alternative to Digital Signatures, by Benaloh, Josh and de Mare, Michael, in EUROCRYPT â93, 1994Â ↩Â ↩^{2}

A note on the low order assumption in class group of an imaginary quadratic number fields, by Karim Belabas and Thorsten Kleinjung and Antonio Sanso and Benjamin Wesolowski, in Cryptology ePrint Archive, Report 2020/1310, 2020, [URL]Â ↩

Secure Accumulators from Euclidean Rings without Trusted Setup, by Lipmaa, Helger, in Applied Cryptography and Network Security, 2012Â ↩

Accountable certificate management using undeniable attestations, by Ahto Buldas and Peeter Laud and Helger Lipmaa, in ACM CCSâ00, 2000, [URL]Â ↩

Utreexo: A dynamic hashbased accumulator optimized for the Bitcoin UTXO set, by Thaddeus Dryja, 2019, [URL]Â ↩

Streaming Authenticated Data Structures, by Papamanthou, Charalampos and Shi, Elaine and Tamassia, Roberto and Yi, Ke, in EUROCRYPT 2013, 2013Â ↩Â ↩^{2}

Compact Accumulator using Lattices, by Mahabir Prasad Jhanwar and Reihaneh SafaviNaini, in Cryptology ePrint Archive, Report 2014/1015, 2014, [URL]Â ↩

ZeroKnowledge Arguments for LatticeBased Accumulators: LogarithmicSize Ring Signatures and Group Signatures Without Trapdoors, by BenoĂźt Libert and San Ling and Khoa Nguyen and Huaxiong Wang, in EUROCRYPT (2), 2016, [URL]Â ↩

LatticeBased Group Signatures: Achieving Full Dynamicity with Ease, by San Ling and Khoa Nguyen and Huaxiong Wang and Yanhong Xu, in Cryptology ePrint Archive, Report 2017/353, 2017, [URL]Â ↩

Vector and Functional Commitments from Lattices, by Chris Peikert and Zachary Pepin and Chad Sharp, in Cryptology ePrint Archive, Report 2021/1254, 2021, [URL]Â ↩

Efficient Accumulators without Trapdoor Extended Abstract, by Sander, Tomas, in Information and Communication Security, 1999Â ↩