yeah I did it on my old G1900 (same mower)
I used an alternator from a BX2360. Internal regulator. Make sure to get the spacer! There is a spacer between the bottom alternator bolt and the block and that is required or the belt won't line up. You'll also have to get the upper adjusting bracket.
wiring is mostly simple if you have any knowledge and have a wiring diagram.
it doesn't just bolt directly on. Well the alternator does in fact bolt directly to the block/head but that's where the "bolt on" ends. You still have to address the wiring. The Dynamo puts out I think 15A, and the wiring is designed for 15A charging. The alternators put out close to 40A (maximum) and when you put 40A through wiring that's designed for 15A you are GOING to have trouble (guaranteed). So what you have to do is run another charge wire from the back of the alternator, through a 50A slow-blow fuse, to the starter. Then disable to original regulator's charging wire (red IIRC), Then you have to change the wiring up on the original regulator, and add a couple wires to the alternator from the original regulator so that the charge lamp works and the alternator's sensing circuit works properly, as well as does away with the factory poor wring to the original regulator. You won't want to have hot wires just hanging out under the dash where the regulator was.
Most of the internally regulator alternators have a total of 3 connections. One is the big terminal (charge wire). Then two spades, one is for the charge lamp in the dash and the other is the voltage sensing, basically it senses system voltage and the internal regulator will adjust it's output accordingly.
also make darn sure to address the grounds. There is a ground from the battery negative to the frame. Remove it and clean it really good. Maybe better to just replace the cable if it's in bad shape. Then there is a smaller jumper wire between the block and the frame. Remove that wire and replace it with a minimum 10ga wire (I used 8ga because I had it). That one is important. The alternator will not work unless it's grounded to the block, which needs to be grounded to the frame since the engine is mounted on rubber mounts. Failure to properly ground the engine to the frame can damage the engine internally. Electricity--regardless of whether it's ground or hot side--is going to take the path of least resistance. If that's through the crankshaft and bearings, that's what it's gonna do. I've seen it happen.
For this reason, if you dont' have much DC electrical knowledge, it's best to just leave the dynamo on it. They work fine, they are stupid simple easy to repair when (if?) the bearings ever go bad, dirt cheap, not in the way of things (much smaller than the internal regulated alternator), and they don't need any wiring modifications unless there is a problem, at that point you just repair what you have (cheaper). The ONLY advantage to alternator is that it is slightly more efficient and will charge a little better at low engine RPM, which again isn't a huge deal since the electrical system on the old G series doesn't need much amperage to run it.