How long was a coach journey from Coburg to St Peterburg in 1790s?

That seems to be an inquiry about how Anna Feodorovna got from being Juliane of Saxe-Coburg-Saalfeld in Bavaria to the Russian Tsar in 1795?

In that case, she travelled overland, by coach for quite a few days.

A description in novel format of that specific journey naming a few stations is found in — Therese Bichsel: "Grossfürstin Anna: Flucht vom Zarenhof in die Elfenau", Schwabe, 2013.

They started on 12 Aug 1795 and arrived two months later.

If the concrete example above shouldn't suffice:

Going by boat from way inland Coburg is not very practical. Nearly all major navigable river systems head North-West, emptying into the North Sea. Going around Denmark would certainly add a huge delay. Only Oder and Vistula are on the way to St Petersburg and flow into the Baltic. That would have been a possibility, but one with questionable advantages. Both rivers add a natural flow again away from the destination by a large degree. You'd also have needed at least change vessels once: embarking on a river boat, then change to sea-worthy.

The theoretical maximum travel speed at the time on land would be achieved by stage coach. Stagecoach travel was designed with speed in mind. Stages would average 60 to 70 miles in one day.

Possible modes of transport would then be coaches, somewhat in the style of a then comfy Berline, a Landauer or whatever style money could afford, perhaps even a very representative Grand Carosse. At that time probably looking like this:

— Friedrich Philipp Reinhold: "Drei Studien einer Reisekutsche"

Around 1806, Napoleon's better half used this:

For ideal conditions in mostly German lands that would have meant up to 100km a day. (— Klaus Beyrer: "Des Reisebeschreibens „Kutsche“. Aufklärerisches Bewußtsein im Postreiseverkehr des 18. Jahrhunderts", in: Wolfgang Griep, Hans-Wolf Jäger (Ed.): "Reisen im 18. Jahrhundert" Winter: Heidelberg, 1986.)

This would make the optimum distance of between 1834 to 2400 km

click on maps for larger view

a roughly 20 day trip. But that optimum could not be achieved in comfort, with entourage (only strictly necessary baggage needed?), excludes sight seeing, diversion, visits, detours, and discounts for the minimum of 4 border crossings

and actual road conditions. These would deteriorate somewhat the farther East the trip gets and would also be reduced in options. Meaning: fairly early on the trip, shortly after crossing the Elbe river. Just adding stages to be on major towns — which would be probably a requirement for higher-up in the social strata passengers — within the modern road system extends easily the journey to much more than 2600 km.

For the first two thirds of the trip, clinging to postal roads would map a trip along these lines:

Setting the first stages most probably at a route from Coburg – Judenbach – Grefenthal – Saalfeld – Neustadt – Gera – Zeitz – Pegau – Leipzig

But as that is a journey through lands of closely connected ancestry, visits to grandmas and uncles would be likley?

Then on to something like this

arriving in the Russian Empire:

For a 'recorded stations' travel route of:
Coburg
–– Leipzig (156 km from Coburg)
–– Torgau (50 km)
–– Frankfurt a.d. Oder (139 km)
–– Küstrin/Kostrzyn nad Odrą (28 km)
–– Landsberg/Gorzow Wielkopolski (43 km)
–– Schneidemühl/Piła (112 km)
–– Bromberg/Bydgoszcz (84 km)
–– Kulm/Chełmno (38 km)
–– Graudenz/Grudziądz (27km)
–– Marienwerder/Kwidzyn (30 km)
–– Braunsberg/Braniewo (93 km)
–– Königsberg/Kaliningrad/Калининград (58 km)
–– Tilsit/Sowetsk/Советск (97 km)
–– Riga (250 km)
–– Dorpat/Tartu (221 km)
–– St Petersburg (270 km)

The resulting map suggests a frame of travel stations to be along these lines:

That means some stops are still missing. The first day of travel very probably did not end in Leipzig, but somewhere on the way. Especially near the end of the journey the distances get too large. For example between Kwidzyn and Braniewo making a stop at Elbing/Elblag would present itself. But between Tartu and St Petersburg, the distance is just too big for a coach to do it in one day. The above route is now calculated to be on modern roads by car to be at least 2028 km (1 day and 8 hours non-stop travel)

For a nice map giving the historic (German) names in the region Prussia, Poland, Lithuania, take a look at the 1796 version available at ChrOnoAtLas (direct-link, below a scaled down to SE-needs 2MB version).

Another stop before Riga would probably be Mitau, as evidenced from being a hub in WikiBooks Baltische Länder: Von der Aufklärung bis zur Entstehung der Nationalstaaten providing for example a bilingual map for Kurland (More maps for Lithuania). And as @Pieter Geerkens noted in comments another likely stop would be the then up and coming city of Schaulen/Siauliai. For mapping the route for the large gap in the final stations it seems indeed likely that the route would be somewhat more closer to the coast.