> Unfortunately, I have missed getting up in the night to let Charlie out
Do you mean that you've slept through the alarm or that you are planning to miss this step out?
At 10 weeks Charlie is unlikely to make it through the night unless you go to bed very late and get up very early. The night time outings are often very good times to instill the 'out to pee' message as they don't really want to play in the dark and cold. I'm sure that as soon as his paws touch the grass, and the chill hits his bladder he'll want to perform for you!
Our timings were final wee at 11pm out at 3am then up at 6.30am. The 3am outing was gradually moved a little each week until he was sleeping through the night but we didn't get past a 6am wake up call until he was 5 months old!!
In the garden try going to the same place each time - he'll recognise the scent and that might stimulate him to go again. You may just have to stand there being uninteresting til he goes. Also if you know he likes to go twice just wait him out. I noticed that our boy always needed several goes to be sure he was empty - he'd start, then get sidetracked by something, and not finish properly. He also developed a kind cute 'wee and walk' routine - so much better than actually stopping to pee!!
Yep, you just have to get used to hanging around in the garden ... Dogs eh!!