Myself... I'd leave it to the pros simply because I could probably figure out a way to do it, but without the proper tools, it'd be haphazard and not a great result. If you get a pro concrete contractor, they'll have a properly sized diamond core bit and a proper core drill to make a clean hole for a better result. You could look into a tool rental/DIY but you might spend the same or more for a likely lesser result anyway. The only real job you need the contractor to do is drill the holes. After that, you could mount the anchors yourself if you like but might be better/easier for them to do that properly while they're on-site anyway.
In urban California finding a good contractor to do that job would be difficult because its a small job. Probably end up with a handyman. The major problem doing it yourself is the rental of the drill and the purchasing the bit. You can't generally rent drill bits. As Joel implied above you could spend more buying the bit and renting the drill than it would cost to have a professional do it.
You may also want someone to look at it to make sure its ok to drill in that part of your deck. Low probability of a problem but is could be an issue.