Leslie and Adrian - Same here - my father is going through a radiotherapy programme at the moment and eating is hard work. Puddings seem to go down better than savoury stuff - everything tastes of nothing much so the softer the texture the less hard work it is. Really really creamy milk puddings (lots of butter and sugar and cream and full cream milk with rice or semolina) or panacotta/creme brulee type desserts pack a lot of calories in for the volume. I think it's much easier to bump up the calorie content of sweet things without changing the taste or texture beyond recognition than it is for the savoury stuff. Even if your father hasn't had much of a sweet tooth up to now, he may be willing to try the puddings - pureed fruit with lots of cream but less sugar could be an alternative in that case. For savoury things - does he eat fish? As long as you get all the bones out before you cook it, white fish baked with breadcrumbs mixed with parsley, grated lemon rind, and melted butter might be worth trying. Although the calorie content by weight is less, the overall nutritional value of fish is very high.
We have found that ginger beer/ale is good - also you might try lemon and ginger tea. I like the snack tray idea - going to give that one some more thought. Finally, check that he hasn't got thrush - that will affect his sense of taste too and could make swallowing painful - and also make sure he's not getting constipated, as that won't help either. Another good reason for keeping the fluids going in, even if nothing much else is.
As I write, one other thought occurs to me. Particularly as he has been through a great deal in the last few weeks - and has gone through a series of losses which really matter to him - I just wonder whether he could be a bit depressed. Might be worth asking your oncologist about that?
Hang on in there - it is really hard to stay on the encouraging rather than nagging side of the line - and try not to let it get to you if he still doesn't eat as much as you would like in spite of all your efforts.