Are there algorithms that can be implemented in this type of systems that do not have known vulnerabilities?
Lots; almost any symmetric system can be implemented in 256k of RAM, and as far as a 16MHz CPU goes, well, that is only an issue if the encryption performance you require is sufficiently high.
If you want recommendations, well, that would depend on what problem you're trying to solve (e.g. are you sending and receiving encrypted traffic, or are you doing something else? Do you have a long term symmetric key you have to use, or is that negotiated by something else periodically/on reboot? What sort of crypto library is available to you? What are your performance requirements?).
Without knowing the answer to that, I am hesitant to give any concrete answer.