I noticed that the Croatian for "gate to heaven" is "vrata raja", "raja" being the genitive singular (rather than dative) of "raj" (heaven). I was wondering how it is in Latin. Is the Latin for "gate to heaven" a literal translation of "gate to heaven" (so, "foris paradiso") or a literal translation of "vrata raja" (so, "foris paradisi")? Also, is there some linguistic reason Croatian and English differ in this regard? English seems a bit more logical in this regard than Croatian.
The most natural way of expressing this would be with the genitive as in the following verse from the Vulgate.
pavensque quam terribilis inquit est locus iste
non est hic aliud nisi domus Dei et porta caeli
Here's another use of the genitive:
Christo apertae sunt portae caeli propter carnalem eius assumptionem. (Irenaeus)
Therefore, given the options you listed, foris paradisi would be better than the alternative.
Is the dative possible?
A question was raised concerning the possible usage of the dative in this way, based on a proverb cited by @d_e in a comment:
porta itineri longissima
However, such usage has been described as "remarkable" and thus would definitely be considered the exception to the rule.
Generally speaking, the dative is associated with the action of a verb, just as is the case with their corresponding expression in English (i.e. prepositional phrases beginning with to). However, in English, the verb is often unexpressed. For example, when we say "the gate to heaven", we understand that to mean "the gate that leads to heaven".
Another possibility is the so-called Dative of Reference. However, when such datives are used to express a local point of view, they are usually used with participles. For example:
oppidum prīmum Thessaliae venientibus ab Ēpīrō
the first town of Thessaly as you come from Epirus.
The Dative of Reference is sometimes also used idiomatically without a verb:
Quō mihi fortūnam? (Hor. Ep. 1.5.12)
Of what use to me is fortune?
In summary, using the dative for porta caelo or foris paradiso seems very questionable at best.