Would it be inappropriate to ask my former manager (which I was on good terms with) to keep an eye out for any future telecommuting positions?
It's perfectly appropriate, though you want to be careful how you phrase your question as, like you say, you don't want to come across as begging for work.
Something like the following should be fine.
When we originally parted ways we looked into the possibility of me continuing to work remotely but that didn't turn out to be a viable option at the time. Since [reasons why you enjoyed working with that manager/team/company], I wonder if you [or the company] would be open to revisiting that idea?
If you know for a fact that they currently have employees working remotely full-time, you can add that as another reason. Consider prefacing your email with generic pleasantries like you would use for any business contact, but don't bother doing so if you don't have anything substantial to add or if you know that your old manager prefers shot and direct communication.
The only time it would be inappropriate is if they gave you valid reasons why telecommuting wasn't an option at the time and you know that it's unlikely that those reasons changed. If the time zone difference between the company and your country is more than a few hours that could be one such reason.
The best way of contacting the manager would probably be via email since it avoids putting him on the spot as a phone call would do. While this doesn't apply to your situation, if you still have a very good or close relationship and occasionally meet up or call each you'd just bring it up during that check-in and ask him to think it over.