Hi. I am new here, registered today so I could reply to this post. I am a surgeon in the UK and my daughter (now 13 weeks old) has a haemangioma (mostly superficial) on her right eyelid. She started oral propranolol three weeks ago, with a moderate response to this - a slight but noticeable decrease in size and lightening in colour. We also started a topical beta-blocker (Timolol eye drops, usually used for glaucoma) two weeks ago and I don't really think that there has been a huge improvement since then.
There are only a few published case studies on the use of topical beta-blockers (or indeed oral propranolol) as the published medical literature takes quite a while to catch up with developments. There has been a lot of discussion at medical conferences about the use of these drugs over the last couple of years though. Timolol will only work on the superficial component of the haemangioma.
Hope that helps....by the way, the only side-effect she gets from the combination of both treatments is occasional cold hands and feet.