An updated listing for these figures and other related conflicts can be found at 25mm/28mm Miniatures for 19th Century European Wars.
It used to be the case that the Franco-Austrian conflict of 1859 and the Risorgimento conflicts of 1860 and later were difficult to find 25mm figures for. Happily, this is no longer the case - almost everything can be purchased from commercial figure manufacturers. The list below is presented as a convenience for those researching figure availability for these conflicts. Note that I am interpreting the term "Risorgimento" quite broadly, to include the Second Italian War of Independence (1859 Franco-Austrian); the actions of the Piedmontese, Garibaldini, Neapolitans, and Papalini in the 1860s; the Italians against the Austrians in 1866; the French, Papalini and Garibaldini in 1867 at Mentana; and finally the Italian actions against Rome and as volunteers in the Franco-Prussian War in 1870.
Ital Model Miniatures: This Italian company produces ranges for Austrians, French, Piedmontese, and Papalini forces. They are not complete, but I believe they are still adding figures to the range. The website is in both Italian and English, although the online catalog has a subtle flaw - if there is no picture for a figure, there is no caption, making it impossible to tell what the figure is! Prices are reasonable, and the sculpting looks fine judging from the pictures. Figures are sold in blisters of 3 or 10 infantry in a single pose, or two guns and 8 crew (4 poses), or 3 command figures in different poses. At the time of this writing, there are no cavalry figures available.
Mirliton: Another Italian company, and well-established, Mirliton has a US distributor, a Spanish distributor (Campaign Game Miniatures - no site listed), a UK distributor (25mm figures available special order), and possibly an Australian distributor (they carry some other Mirliton lines, so this range may be available by special order). Mirliton makes Austrians, Piedmontese, Garibaldini, Neapolitans, and Papalini. Ranges include infantry, command, mounted generals and personality figures, and cavalry. Prices are reasonable, and the sculpting is excellent. Figures are available individually or in unit packs of various sizes (35 or 50 infantry, 15 cavalry).
Battle Honours: Battle Honours produces a range of French and Austrians which are also available in the US from 19th Century Miniatures. The ranges include Austrian infantry, cavalry, artillery, and mounted command for 1859 and 1866, and French infantry, foot guard, and artillery for 1859 (and, by extension, 1867 and 1870). The range is no longer being sculpted, but is fairly extensive. Sculpting is excellent - figures come in packs of 24 infantry (including command), 8 cavalry, or 3 guns and twelve crew. Prices are reasonable.
Wargames Foundry: Wargames Foundry does not make a dedicated range for this period, but has an extensive Franco-Prussian range which is a good source for many of the French cavalry figures which are otherwise unavailable, although care should be taken that the 1859 uniforms are the same as those of the figures ordered. Also, French high command is available, and the "Mexican Soldiers Command" pack from their Mexican range is useful for the mounted general figure. While there are French figures in their Crimean range, these are not extremely suitable for the later conflicts - and, although some would say otherwise - they mostly cannot be used as Italians, either. Check your uniforms carefully before ordering. While Foundry figures are quite expensive, they are not only fabulous sculpts, but the frequent sales and various deals mean they can often be purchased at less than the full price.
Frontier: Austro-Prussian, Franco-Prussian, and Crimea ranges may be useful for various figures. There has been much talk about the availability and non-availability of these ranges - the URL here takes you to the Haus of Stuff, which is now managed by Tactical Edge, the current owner of these figure lines (so far as I can discover...). I include these ranges here for the sake of completeness, assuming that they either are or will be available again in the near future. The figures are perhaps a bit smaller than other ranges listed here, but are also considerably less expensive (30 figures for about $20.00 USD).
Eureka Miniatures: This Australian company makes some figures which may be useful: aside from the 1864 Danes which are outside our scope here, they make 1864-66 Austrians, and some foot figures for the Franco-Prussian War. Note that these figures are listed as 28mm on the site. Scultping is excellent, and they have various distributors in the UK (Fighting 15s) and the US (Brigade Games, although these figures may be special order). Brigade games also has female zouves for adding gender variation to your Garibaldini units...
Castaway Arts: Another Australian company which produces a Franco-Prussian line, they have foot, guard, some cavalry (chasseurs d'afrique) and mounted officer/general figures useful for 1859. Figures are available individually - they are a bit pricey, but sculpting is very nice.
Timeline will be producing the old Helion Austro-Prussian range, to be available soon (Fall-Winter 2005). Apparently, they have been having some difficulty with their website and e-mail.
Askari Miniatures: There are some useful turcos and zouaves available from this company, and possibly some other figures. Beautiful sculpting - the focus of the company seems to be Morocco in the 1920s, but these figures would be great for a lot of earlier periods as well. Infantry packs are 8 figures for $14.00 (USD) with 6 mounted for about $20.00. Packaging and pricing varies with different sets. They are US-based, but partner with Chiltern Miniatures in the UK and Uchronie in France. (Thanks to B. Checota for the tip.)
Anyone who knows of other 25mm figures for this period should contact me with information.