Please suggest any timeline in which motorcycles or similarly modified vehicles can be carriers for HMG, SAM's, mortars, rocket launchers etc and what would these vehicles look like and what can they realistically deploy
...Can be carriers? Our timeline. The Italian Bersaglieri had 500-cc, 13-HP to 18-HP tricycles in use in WWII. Unlike a sidecar, the paired wheels were the back ones, on one axle. You could fire a HMG from the load platform, and there were modifications with a pintle mount for a light AAMG. You could carry a mortar, but not the heaviest ones, and you wouldn't fire from the platform an 81mm; maybe a 45mm. You could of course carry a WWII-era LAW of any kind, and you could probably fire them from the platform. They could tow (at slow speed) a 47mm ATG. There was a version that could be disassembled, and it was allocated to the Italian air-landing division, the Divisione La Spezia.
But if the question is a timeline in which such vehicles should be carriers - then the answer is none. Such a vehicle, like a motorcycle-sidecar combo, needs something of a half-decent dirt road, however narrow, to be valuable; at that point, a true fully tracked, lightly armored weapon carrier is better, and it can move on that narrow half-decent dirt road and off it with sufficient effectiveness and reliability.
Yeah, it will be slower than the motorcycle-tricycle-combo on a good road, but that's secondary; and anyway on a good road you can use a decent four-wheel truck for your Toyota War.
Additionally, the unarmored motorcycle-tricycle-combo and the unarmored Toyota wartruck don't survive the first MG burst that hits them, while the armored carrier might well do. And even if you really want to spare money on the armor, you can go for an unarmored, but tracked vehicle, from the Kettenkrad to the Bandvagn.