Hi, I'm Dr. Jill. Unfortunately there are a wide variety of things that can cause Alpaca's to not be able to stand from a whole body illness making them too sick and too weak to be willing to get up, to a spinal cord injury or mass impinging on the spinal cord inhibiting their legs from working correctly, to an injury to a leg.
I wish I could offer you more options for things to do at home, but because of the wide range of things that can cause these signs and the seriousness of not being able to get up, I would definitely recommend that you enlist the help of your regular veterinarian who can perform a full physical exam and potentially narrow down the possible issues.
Some things you can look at to help gauge the severity of systemic (whole body) illness are the color of his gums (should be pink and moist) and the capillary refill time (how long it takes the color to come back when you press on the gums), his rectal temperature (should be around 100.5-102.5 F), his appetite and willingness to drink water, and whether or not he's able to move his legs himself as well as any swelling on his legs or back or any pain elicited when to you feel those areas.
Some viral infections such as West Nile can cause alpacas to go down as well as some parasite infestations present in some areas of the country that migrate through their nervous system.
Certainly intestinal upset, other infections, or trauma can cause them to go down as well.
At home, you can keep food and water accessible as well as continue to encourage him to stand and continue moving his limbs through their normal range of motion several times a day to maintain mobility if this does not appear to elicit pain from a possible injury. You can also attempt to rig a sling to hold him temporarily though if he is not able to bear weight on his own he cannot stay in this for long periods of time (it will cause pressure sores).
The longer he stays down as well, the less likely you will be able to get him up again, regardless of the cause.
This is one big reason to enlist your regular vets help now to give him the best chance of recovery.
I hope this provides some useful information for you. If you have any additional questions or there is any way I can assist further, please let me know...I would be happy to do so.