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Do any of then have a tonal accent ala the Scandinavian langs? From the little bit I've researched and listened to of Finnish, my first impulse would be no. But I'd like to be certain.

Wikipedia says Livonian has a system similar to Danish stød.

From http://en.wikipedia.org/wiki/Chroneme :

Estonian and Sami also have a three-way [length] distinction in consonants, e.g. lina "bed sheet", linna (half-long 'n') "of the city", linna (over-long 'n') "to the city". Estonian, in which the phonemic opposition is the strongest, uses tonal contour as a secondary cue to distinguish the two; "over-long" is falling as in other Finnic languages, but "half-long" is rising.

Livonian may indeed be the best bet here. The glottal tone (from original open stress'd syllables, as in *apu "help" /aʔb/, or from coda *h, as in *rihma "string" /ri:ʔm/) does resemble Danish, but the system in general is supposedly rather closer to the Baltic systems. (Lithuanian has a "broken tone" which also involves glottalization).[/size] There's a split of original vowels to 2-3 lengths* depending on the root structure and AIUI these have different prosodic features as well (stress is still initial tho).

—Outside the Baltic area, pretty much everything is toneless with boringly regular initial stress too, though the Mordvinic languages have somewhat mobile stress. (Aaand I suppose there might have been some obscure Selkup dialect that died in 1912 but had 12 tones, as detail'd info on the Samoyedic langs still isn't too plentiful.)

*Three lengths only for *e *o and only technically then too: original *e: *o: /i:e u:o/, but with secondary lengthening, /je wo/.)

KHS wrote:From http://en.wikipedia.org/wiki/Chroneme :

Estonian and Sami also have a three-way [length] distinction in consonants, e.g. lina "bed sheet", linna (half-long 'n') "of the city", linna (over-long 'n') "to the city". Estonian, in which the phonemic opposition is the strongest, uses tonal contour as a secondary cue to distinguish the two; "over-long" is falling as in other Finnic languages, but "half-long" is rising.

If we want to consider that phonological (and not just to do with the phonetic realization of particular contrasts), then that'd be a lexical tone, like Hausa or Mandarin, rather than lexically-specified pitch accent, like Swedish or Japanese.