Is "certainly possible" an oxymoron?

No, it's a sensible phrase that tells you two separate things: a) the speaker believes X is possible, b) the speaker is emphasizing a very high level of certainty about this belief.

There's no apparent contradiction necessary for an oxymoron because certainty and possibility are different, non-exclusive, non-dependent things. We can give an example for every combination of a level of certainty and a level of possibility:

• Solar powered air travel is certainly possible. It's not commercially viable yet, but there's a concept plane that proves it can be done.
• Hoverboards are probably possible, but I don't know how they could work except over a magnetic surface.
• Teleportation might be possible. There are a couple of mechanisms by which it theoretically might work, but it might well not actually be possible to engineer, though it's hard to see how this impossibility could ever be proved. For the foreseeable future, it'll remain a definite maybe.
• Time travel is probably impossible, it barely makes logical sense. But I'd love to be proved wrong.
• Perpetual motion machines are certainly impossible, they defy fundamental laws of physics.

Of course in day to day use, the phrase "certainly possible" is usually more about subtext, often in the context of "That's certainly possible, but not easy", where the certainty about the possibility is contrasted with some complicating factor or caveat, often to stress willingness (implying "I'm not trying to be awkward here and I do absolutely 100% agree that X is possible, but...").

For example:

• You'd like to change your booking? Of course, I'll do that right now [this is easy and routine]
• You'd like to change your booking? That's certainly possible, I'll just talk you through the procedure [I'm extremely confident it can be done, but there might be complications that might make you reconsider your choice. I'm stressing the fact it's definitely possible so you know that I'm happy to go through those complications if that's your choice, so that you don't think I'm being obstructive or trying to talk you out of it]
• You'd like to change you booking? That's probably possible, I'll just check with my supervisor [I'm not completely confident that it can be done, you should start thinking about what you will do if it is not possible]

"Certainly probable" could be argued as being an oxymoron, because like the popular oxymoron "Definitely maybe", both parts relate to probability or certainty.

But probability and possibility are different things. Successfully arguing that "certainly possible" is an oxymoron is probably impossible ;-).

No, the "certainly" modifies the possibility, meaning that it's certain that there's a non-zero probability of the event's occurrence.

I don't think it is an oxymoron. The 'certainly' does not apply to the thing that is possible - it relates to the judgement of the speaker.

Example

So you want to build a tunnel through the mountain? I don't believe that is physically possible.

Oh I am certain it is possible - it just requires sufficient investment.

OR

Oh it is certainly possible - it just requires sufficient investment.

I'll disagree with the other answers and argue that it is an oxymoron, in the same way that jumbo shrimp, awfully good, pretty ugly, and other classic oxymorons are. Oxymoron does not mean contradiction, it means:

a figure of speech by which a locution produces an incongruous, seemingly self-contradictory effect, as in “cruel kindness” or “to make haste slowly.”.

Note the use of the word seemingly. I think certainly possible qualifies.

Adding for emphasis: the phrase "certainly possible" seems to me to have the same constructive logic as "pretty ugly" or "awfully good", both of which are recognized by every list of oxymorons I looked at as being oxymorons.