Is it ethical to present a second paper at a conference when the first paper and travel was funded by a separate organization?

I can't see any ethical issues at all. You seem to be properly fulfilling the obligations of your funding. What else you do at a conference is your own concern. The funders are willing to support you and you are doing what is required for the funding. Rest easy.

I can't imagine that any funding agency would suggest (or even think) that you can't do other things at a conference. They certainly expect you to take advantage of the opportunities it affords.

Asking "is X ethical" is a philosophical question, since it depends on the notions of morality and justice you approach the question with. It's impossible to truly answer the question without starting with axioms to that effect. What is considered ethical to one person may be considered wholly unethical to another. Academia in general has no prescribed code of ethics- there may be expectations or general consensus about what is right or wrong, but reasonable people can still disagree with the consensus for any number of reasons.

I think a better way to phrase the question would be, "In a professional academic setting, am I likely to get into trouble for X, or would I be looked down by my peers for X (regardless of whether I get into trouble)?"

In answer to the rephrased question, my professional opinion would be that your actions are perfectly reasonable, rational, and justifiable, and I believe most people would feel the same way. Unless, of course, your funding agreements specifically stated that your desired course of action is forbidden in this case, which might itself be reasonably interpreted as an unethical stipulation.

Questions of ethics generally revolve around conflicts of interest, where your personal interests pull you in a direction that is in opposition to your professional or moral obligations.

In this case, your professional obligation is to present paper #1 at this conference, and your personal interest is to present paper #2 at the conference. Assuming you have the time available to present both, and furthermore that the second doesn't undermine your employer's interests in some way--which I'll take as a given, since you said the two are entirely unrelated--there doesn't appear to be any conflict here, and so no ethical problems.