There definitely are ways to determine noun gender in swedish. Just note that there usually are a few exceptions to all these rules.
Practically all nouns that end in -a have common gender. En tavla, en kaka, en flaska. All of these have plural -or as well.
Some exceptions to this are the bodyparts ett öga, ett hjärta, ett öra. And the word 'ett schema'
Nouns ending in -(n)ing usually have common gender, as well as plural -ar.
Nouns ending in -are, -dom, -else, -het, -ion, -ism and -nad are almost always common gender as well.
Examples En lärare, en domare, en sjukdom, en ungdom, en rörelse, en styrelse, en personlighet, en hemlighet, en spion, en station, (en) socialism, (en) turism, en skillnad, (en) vördnad.
Som exceptions are ett altare, ett fängelse, ett landsting
Nouns ending in -eri and -um are almost always of neuter gender. Ett gymnasium, ett album, ett museum, ett bageri, ett batteri.
Exceptions include 'en selleri'
Hope that was helpfull. By now I instinctively know these, but in the beginning i memorized a few of these rules. I took some of the examples from a dutch book on swedish grammar. "Van Dale Grammatica Zweeds". It's nice to have such a book so that you're able to quickly look at a comprehensive guide on all the grammar.