No, the rules say that ANY water or fire type is allowed, because by default they are supposed to be beach- or summer-related. The classification of other Pokemon allowed is based in their relation to the Sun.
So, I think having water and fire types in your list is redundant, because you'll have to have EVERY water and fire type. Just say that all of 'em are allowable, and make a list instead if the other, non-Water and non-Fire types that can be related to the beach.
Some examples are: Solrock (because it's the sun, literally), Espeon (it's called the SUN Pokemon), several grass types, such as Tropius, Venusaur and Exeggutor, which are tropical plants, as well as things like Sawbuck and Tangrowth which have Chlorophyll as an ability. Some Bug or Rock types that are found on the beach are also fine, like Armaldo and stuff. You get the idea.
EDIT: Ninjask'd by Swampy. Well, Ninjask being a Cicada is also related to summer, so there ya go.