I've been mulling it over and I think you could carry my changes from SW:CW Risk to standard risk. At least if you have one of the latest versions with actual men and horses and cannons.
Here's what to do.
Forget about the cards, except may be as a way to randomly pick a starting country. Each person starts as one country, with 20 men, 5 horses and 3 cannons. Again, each country is worth 1 point. You count your points at the start of your turn to see how many new units you can have. If you don't have a unit on a country, you don't get a point for it. The exception to this will be in the continental control rule, below. Men cost 1 point and use the d6. Horses (cavalry) cost 3 points, but use the d8. Cannon cost 5 points, use the d6 but allow you to bring an extra unit into the order of battle.
Changes to combat - as in normal Risk, the attacker may roll up to three die. Which die he rolls depends on which units from the attack he is including in the order of battle. If he includes a cannon (1 or more) he may add one d6 more, increasing his maximum to four units and 4 die. This applies likewise to the defender, who normally rolls 2 die, but may add a cannon and extra d6.
As normal risk, each rolls his dice and compares highest results. In the event of a tie, the defender wins. The player who has lost a piece chooses which piece to remove from the pieces in the order of battle (i.e. the ones used to determine which die to roll). Other units are considered reserves, which may be brought up on the next round to bolster your order of battle.
As the attacker, you may withdraw so long as you launched your attack from an adjacent country. You may not withdraw along shipping lines (marines always have it rough). If you withdraw, all of your units must return to a friendly territory (one you already control) from which some of your force must have come. You may withdraw after removing casualties and before rolling die for the next round has commenced.
Continent Rules - If, at the start of your turn, you control a whole continent (Australasia, say) you get the bonus production normal for that continent (2 for Australia, I believe). If you have achieved control of a continent, you no longer need to occupy each country to receive its production, you will receive all production for the continent (and the bonus). If, however, someone should "break" your continent, these unoccupied countries return to neutral status until they are later occupied. Before continental domination maybe declared, you must have had at least one unit in each country of the continent at the start of your turn. I think. I'm waffling on continents ATM.
Supply rules - you get a point for each country you control, to spend on new units, at the start of your turn. If you don't have a unit in a country, you don't get a point for it (obvious, I know) - but don't let that stop you. You may withdraw all of your troops from a country.